# LICS 2011 Accepted Papers with Abstracts

Juha Kontinen, Antti Kuusisto, Peter Lohmann and Jonni Virtema. Complexity of two-variable Dependence Logic and IF-Logic
Abstract: We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are NEXPTIME-complete, whereas for IF^2, the problems are Pi^0_1 and Sigma^0_1 -complete, respectively. We also show that D^2 is strictly less expressive than IF^2 and that already in D^2 infinity and equicardinality of two unary predicates can be expressed.
Decidability of Definability
Abstract: For a fixed infinite structure Gamma with finite signature tau, we study the following computational problem: Input are quantifier-free first-order tau-formulas phi_0,phi_1,...,phi_n that define relations R_0,R_1,...,R_n over Gamma. The question is whether the relation R_0 is primitive positive definable from R_1,...,R_n, i.e., definable by a first-order formula that uses only relation symbols for R_1,..., R_n, equality, conjunctions, and existential quantification (disjunction, negation, and universal quantification are forbidden).

We show decidability of this problem for all structures Gamma that have a first-order definition in an ordered homogeneous structure Delta with a finite language whose age is a Ramsey class and determined by finitely many forbidden substructures. Examples for structures Gamma with this property are the order of the rationals, the random graph, the homogeneous universal poset, the random tournament, all homogeneous universal C-relations, and many more. We also obtain decidability of the problem when we replace primitive positive definability by existential positive, or existential definability. Our proof makes use of universal algebraic and model theoretic concepts, Ramsey theory, and a recent characterization of Ramsey classes in topological dynamics.
The Computational Meaning of Probabilistic Coherence Spaces
Abstract: We study the probabilistic coherent spaces --- a denotational semantics interpreting programs by entire functions taking scalars on the non negative real numbers. We prove that this semantics is adequate for a probabilistic extension of pure lambda-calculus: the probability that a term reduces to a head normal form is equal to the sum of the scalars of its denotation on a suitable set of values. The result gives, in a probabilistic setting, a quantitative refinement to the adequacy of Scott's model for untyped lambda-calculus.
Richard Mayr and Parosh Abdulla. Computing Optimal Coverability Costs in Priced Timed Petri Nets
Abstract: We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a
real-valued clock. Transition arcs are labeled with time intervals,
which specify constraints on the ages of tokens.
Our cost model assigns token storage costs per time unit to places,
and firing costs to transitions.
We study the cost to reach a given control-state.
In general, a cost-optimal run may not exist. However,
we show that the infimum of the costs is computable.
Yijia Chen and Jörg Flum. Listings and logics
Abstract: There are standard logics DTC, TC, and LFP capturing the complexity classes L, NL, and P on ordered structures, respectively. In [Chen and Flum, 2010] we have shown that LFP_inv, the order-invariant least fixed-point logic LFP,'' captures P (on all finite structures) if and only if there is a listing of the P-subsets of the set TAUT of propositional tautologies. We are able to extend the result to listings of the L-subsets (NL-subsets) of TAUT and the logic DTC_inv (TC_inv). As a byproduct we get that LFP_inv captures P if DTC_inv captures L.

Furthermore, we show that the existence of a listing of the L-subsets of TAUT is equivalent to the existence of an almost space optimal algorithm for TAUT. To obtain this result we have to derive a space version of a theorem of Levin on optimal inverters.
Noncomputable conditional distributions
Abstract: The use of probability to reason about uncertainty is fundamental to modern science and AI, and the computation of conditional probabilities, in order to perform evidential reasoning in probabilistic models, is perhaps its single most important computational problem.  The desire to produce increasingly complex probabilistic models has led to renewed interest in probabilistic programming languages, in which practitioners can define intricate, even infinite-dimensional, models by implementing a generative process that produces an exact sample from the joint distribution.  Implementations of these languages have endeavored to provide general algorithmic support for conditional distributions with respect to continuous random variables, but these efforts have remained ad-hoc and incomplete.  Here we demonstrate why this support is necessarily incomplete, by exhibiting a computable joint distribution with a noncomputable conditional distribution.  Specifically, we construct a pair of computable random variables (X,Y) in the unit interval whose conditional distribution P[Y|X] encodes the halting problem.

Nevertheless, probabilistic inference has proven remarkably successful in practice, even in infinite-dimensional continuous settings.  We prove several results giving general conditions under which conditional distributions are computable.  In the discrete or dominated setting, under suitable computability hypotheses, conditional distributions are computable.  Likewise, conditioning in abstract topological settings is a computable operation, in the presence of certain additional structure, such as independent absolutely continuous noise.
The Complexity of Verifying Ground Tree Rewrite Systems
Abstract: Ground tree rewrite systems (GTRS) are an extension of pushdown systems
with the ability to spawn new subthreads that
are hierarchically structured.
In this paper, we study the following problems over GTRS:
(1) model checking EF-logic, (2)
weak bisimilarity checking against finite systems, and (3) strong bisimilarity
checking against finite systems. Although they are all known to be decidable,
we show that problems (1) and (2) have nonelementary complexity, whereas
problem (3) is shown to be in $\coNEXP$ by finding a syntactic fragment of EF
whose model checking complexity is complete for $\P^\NEXP$.
The same problems are studied
over a more general but decidable extension of GTRS
called regular GTRS (RGTRS), where regular rewriting is allowed. Over RGTRS
we show that all three problems have nonelementary complexity.
We also apply our techniques to problems over PA-processes, a well-known class
of infinite systems in Mayr's PRS (Process Rewrite Systems) hierarchy. For
example,
strong bisimilarity checking of PA-processes against finite systems is shown
to be in
$\coNEXP$, yielding a first elementary upper bound for this problem.
Abstract: Abstract—We study finite tree automata running over infinite binary trees. As usual, a run of such an automaton over an input tree is a tree labeled by control states of the automaton: the labelling is built in a top-down fashion and should be consistent with the transitions of the automaton. A branch in a run is accepting if the ω-word obtained by reading the states along the branch satisfies some acceptance condition (typically an ω-regular condition such as a Büchi or a parity condition). Finally, a tree is accepted by the automaton if there exists a run over this tree in which every branch is accepting. In this paper, we consider two relaxations of this definition introducing a qualitative accept.

First, we relaxe the notion of accepting run by allowing a negligible set (in the sense of measure theory) of non-accepting branches. In this qualitative setting, a tree is accepted by the automaton if there exists a run over this tree in which almost every branch is accepting. This leads to a new class of tree languages, qualitative tree languages. This class enjoys many good properties: closure under union and intersection (but not under complement), emptiness is decidable in polynomial time, strong relation with Markov decision process.

The second one, is by replacing the existential quantification — a tree is accepted if there exists some accepting run over the input tree — by a probabilistic quantification — a tree is accepted if almost every run over the input tree is accepting. For the run, we may use either classical acceptance or qualitative acceptance. In particular, for the latter, when equipped with a Büchi condition, we show that it leads to a class of probabilistic automata on infinite trees enjoying a decidable emptiness problem. To our knowledge, this is the first positive result for a class of probabilistic automaton over infinite trees.
A tetrachotomy for positive first-order logic without equality
Abstract: We classify completely the complexity of evaluating positive equality-free sentences
of first-order logic over a fixed, finite structure D. This problem may be seen as a
natural generalisation of the quantified constraint satisfaction problem QCSP(D). We obtain
a tetrachotomy for arbitrary finite domains: each problem is either in L, is NP-complete,
is co-NP-complete or is Pspace-complete. Moreover, its complexity is characterised algebraically
in terms of the presence or absence of specific surjective hyper-endomorphisms; and, logically,
in terms of relativisation properties with respect to positive equality-free sentences.
We prove that the meta-problem, to establish for a specific D into which of the four
classes the related problem lies, is NP-hard.
Formalizing Randomized Matching Algorithms
Abstract: Using Jeřábek's framework for probabilistic reasoning, we formalize the correctness of two fundamental RNC2 algorithms for bipartite perfect matching within the theory VPV for polytime reasoning. The first algorithm is for testing if a bipartite graph has a perfect matching, and is based on the Schwartz-Zippel Lemma for polynomial identity testing applied to the Edmonds polynomial of the graph. The second algorithm, due to Mulmuley, Vazirani and Vazirani, is for finding a perfect matching, where the key ingredient of this algorithm is the Isolating Lemma.
Temporal Specifications with Accumulative Values
Abstract: There is recently a significant effort to add quantitative objectives to formal verification and synthesis.
We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications.

In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with
the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the
{\em prefix-accumulation assertions\/} $\Sum(v) \geq c$ and $\Avg(v) \geq c$, where $v$ is a numeric variable of the system, $c$ is a constant
rational number, and $\Sum(v)$ and $\Avg(v)$ denote the accumulated sum and average of the values of $v$ from the beginning of the computation
up to the current point of time. We also allow the {\em path-accumulation assertions\/} $\LimInfAvg(v)\geq c$ and $\LimSupAvg(v)\geq c$,
referring to the average value along an entire computation.

We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation  assertions may be refined with controlled-accumulation'', allowing, for example, to specify constraints on the average waiting time between a request and a grant.
On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.
Continuous Random Variables
Abstract:   We introduce the domain of continuous random variables (CRV) over a
domain, as an alternative to Jones and Plotkin's probabilistic
powerdomain.  While no known Cartesian-closed category is stable
under the latter, we show that the so-called thin CRVs define a strong
monad on the Cartesian-closed category of bc-domains.  The Jones and
Plotkin semantics of higher-order probabilistic programs occurs as a
form of extensional collapse of our new semantics in terms of thin
CRVs, preserving observational equivalence.  We apply this to solve
a recent problem posed by M. Escard\'o [note: proof not complete as
of Tuesday, Jan 04, 13h; claim may be removed from final
submission].  Thin CRVs arose from the study of the second author's
(layered) Hoare indexed valuations, and we also make the connection
apparent.
Sergey Goncharov and Lutz Schröder. Powermonads and Tensoring Unranked Effects
Abstract: Both in semantic theory and in programming practice, algebraic
concepts such as monads or, essentially equivalently, (large)
Lawvere theories are a well-established tool for modelling generic
side-effects. An important issue in this context are combination
mechanisms for such algebraic effects, which allow for the modular
design of programming languages and verification logics. The most
basic combination operators are sum and tensor: while the sum of
effects is just their non-interacting union, the tensor imposes
commutation of effects. However, for effects with unbounded arity,
such as continuations or unbounded non-determinism, it is not a
priori clear whether these combinations actually exist in all
cases. Here, we introduce the class of uniform effects, which
includes unbounded non-determinism and continuations, and prove that
the tensor does always exist if one of the component effects is
uniform, thus in particular improving on previous results on
tensoring with continuations. We then treat the case of (unbounded)
non-determinism in more detail, and give an order-theoretic
characterization of effects for which tensoring with non-determinism
is conservative, thus enabling non-deterministic arguments for
deterministic programs such as a generic version of the
Silvain Rideau and Glynn Winskel. Concurrent strategies
Abstract: A bicategory of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate.  Games and strategies are represented as polarized event structures, in which
polarities distinguish the moves of Player and Opponent.  A total map of polarized event structures into $A$ can be understood as a pre-strategy in a game $A$---the map ensures that Player and Opponent respect the constraints of the game.  Following Joyal, a pre-strategy from a game $A$ to a game $B$ is understood as a pre-strategy in a composite game got by setting the dual game of $A$, reversing the roles of Player and Opponent, in parallel with $B$.  From this general scheme concurrent strategies---pre-strategies for which copy-cat strategies behaves as an identity w.r.t.~composition of pre-strategies---are characterized as those pre-strategies which satisfy the two conditions of receptivity and innocence. It is shown how (bi)categories of stable spans, certain profunctors, Berry's stable functions, and certain sequential algorithms arise as sub(bi)categories of concurrent games.  It is indicated how the results can be adapted to other models such as asynchronous transition systems and Mazurkiewicz trace languages, which leads to a brief comparison with related work.
Languages of Dot-Depth One over Infinite Words
Abstract: We extend languages of dot-depth one to infinite words. As for
finite words, this class of languages corresponds to the Boolean
closure of Sigma1 of the first level of the quantifier alternation
hierarchy of first-order logic FO[<,+1,min,max]. We give a decidable
characterization of the Boolean closure of Sigma1[<,+1,min]
over infinite words; here, the max-predicate is void.
Our characterization is a  combination of Knast's algebraic property
for dot-depth one  and a topological condition.  This yields decidability
of the problem whether a given regular omega-language has
dot-depth one.

Our approach considers finite and infinite words simultaneously. We
prove decidable characterizations for the Boolean closure of
Sigma1[<,+1,min] as well as for the Boolean closure of
Sigma1[<,+1,min,max] over finite and infinite words. In this
setting, the max-predicate can be used for distinguishing between
finite and infinite words. Hence, our result on infinite words can be
obtained as a corollary.

This paper is self-contained and we give full proofs. In particular,
a new combinatorial proof of Knast's Theorem concerning languages of
dot-depth one over finite words is included.
Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma
Abstract: Dickson's Lemma is a simple yet powerful tool widely used in decidability proofs, especially when dealing with counters or related data structures in algorithmics, verification and model-checking, constraint solving, logic, etc.  While Dickson's Lemma is well-known, most computer scientists are not aware of the complexity upper bounds that are entailed by its use.  This is mainly because, on this issue, the existing literature is not very accessible.

We propose a new analysis of the length of bad sequences over (N^k,<=), improving on earlier results and providing upper bounds that are essentially tight.  This analysis is complemented by a "user guide" explaining through practical examples how to easily derive complexity upper bounds from Dickson's Lemma.
The Ultimate Undecidability Result for the Halpern-Shoham Logic
Abstract: The Halpern-Shoham logic is a modal logic of time intervals. Some effort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisfiability problem. We close this classification by showing -- what we believe is quite an unexpected result -- that the  logic of subintervals, the fragment of the Halpern-Shoham  where only the operator "during", or D, is allowed, is undecidable over discrete structures.
This is surprising as this, apparently very simple, logic is decidable over dense orders and its reflexive variant is known to be  decidable over discrete structures.
Our result subsumes a lot of previous negative results for the discrete case, like the undecidability for ABE, BD, ADB, AAbarD, and so on.
Nikos Tzevelekos and Andrzej Murawski. Game semantics for good general references
Abstract: We present a new fully abstract and effectively presentable
denotational model for RefML, a paradigmatic higher-order programming
language combining call-by-value evaluation and general references in
the style of ML. Our model is built using game semantics. In contrast
to the previous model by Abramsky, Honda and McCusker, it provides a
faithful account of reference types, and the full abstraction result
does not rely on the availability of spurious constructs of reference
type (bad variables). This is the first proper denotational model of
this kind, preceded only by the trace model recently proposed by Laird.
A type system for complexity flow analysis
Abstract: We propose a type system for an imperative programming language, which certifies program time bounds. This type system is based on language information flow security approach. Each program variable has a level and we prevent information from flowing from low level variables to high level variables. Moreover, we introduce a downgrading mechanism in order to delineate a broad class of programs. Thus, we establish the first relation between security-typed language and implicit computational complexity. We establish a characterization of the class of polynomial time functions.
To our knowledge, this is the first type system for an imperative language, which provides a complete characterization of polynomial time functions.
Christian Herrmann and Martin Ziegler. Computational Complexity of Quantum Satisfiability
Abstract: Quantum logic generalizes, and in dimension one coincides with, Boolean propositional logic.
We introduce the weak and strong satisfiability problem for quantum logic formulas; and show both NP-complete in dimension two as well.
For higher-dimensional spaces R^d and C^d with d>2 fixed, on the other hand, we show the problem to be complete for the nondeterministic Blum-Shub-Smale model of real computation.
This provides a unified view on both Turing and real BSS complexity theory;
and adds (a perhaps more natural and combinatorially flavoured) one to the still sparse list of NP_R-complete problems, mostly pertaining to real algebraic geometry.
Our proofs rely on (a careful examination of) works by John von Neumann as well as contributions by Hagge et.al (2005,2007,2009).
We finally investigate the problem over INdefinite finite dimensions and relate it to NONcommutative semialgebraic geometry.
Isomorphisms of types in the presence of higher-order references
Abstract: We investigate the problem of type isomorphisms in a programming language with higher-order references. We first recall the game-theoretic model of higher-order references by Abramsky, Honda and McCusker. Solving an open problem by Laurent, we show that two finitely branching arenas are isomorphic if and only if they are geometrically the same, up to renaming of moves (Laurent's forest isomorphism). We deduce from this an equational theory characterising isomorphisms of types in a finitary programming language L2 with higher order references. We show however that Laurent's conjecture does not hold on infinitely branching arenas, yielding a non-trivial type isomorphism in the extension of L2 with natural numbers.
Lars Birkedal, Rasmus Ejlers Møgelberg, Jan Schwinghammer and Kristian Støvring. First steps in synthetic guarded domain theory: step-indexing in the topos of trees
Abstract: We present the topos S of trees as a model of guarded recursion.  We
study the internal dependently-typed higher-order logic of S and show
that S models two modal operators, on predicates and types, which
serve as guards in recursive definitions of terms, predicates, and
types.  In particular, we show how to solve recursive type equations
involving dependent types.  We propose that the internal logic of S
provides the right setting for the synthetic construction of abstract
versions of step-indexed models of programming languages and program
logics.  As an example, we show how to construct a model of a
programming language with higher-order store and recursive types
entirely inside the internal logic of S.
A decidable two-way logic on data words
Abstract: We study the satisfiability problem for a logic on data words. A data word is a finite word where every position carries a label from a finite alphabet and a data value from an infinite domain. The logic we consider is two-way, contains  "future" and "past" modalities, where these are considered as reflexive and transitive relations, and data equality and inequality tests. This logic corresponds to the fragment of XPath with the 'following-sibling-or-self' and 'preceding-sibling-or-self' axes over a data word. We show that this problem is decidable,  ExpSpace-complete. This is surprising considering that with the strict navigation relations (non-reflexive) the satisfiability problem is undecidable. To show this we first reduce the problem to a derivation problem for an infinite transition system, and then we show how to abstract this problem into a reachability problem of a finite transition system.
Martin Churchill, James Laird and Guy McCusker. Imperative Programs as Proofs via Game Semantics
Abstract: Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. We can embed intuitionistic first-order linear logic into this system, as well as an imperative total programming language. The logic makes explicit use of the fact that in the game semantics the exponential can be expressed as a final coalgebra. We establish a full completeness theorem for our logic, showing that every bounded strategy is the denotation of a proof.
Davide Bresolin, Angelo Montanari, Pietro Sala and Guido Sciavicco. What's decidable about Halpern and Shoham's interval logic? The maximal fragment ABBL
Abstract: The introduction of Halpern and Shoham's modal logic of intervals (later on called HS) dates back to 1986. Despite its natural semantics, this logic is undecidable over all interesting classes of temporal structures. This discouraged research in this area until recently, when a number of non-trivial decidable fragments have been found.
This paper is a contribution towards the complete classification of HS fragments. Different combinations of Allen's interval relations begins (B), meets (A), and later (L), and their inverses Abar, Bbar, and Lbar, have been considered in the literature.
We know from previous work that the combination ABBbarAbar is decidable over finite linear orders and undecidable everywhere else. We extend these results by showing that ABBbarLbar is decidable over the class of all  (resp., dense, discrete) linear orders, and that it is maximal w.r.t decidability over these classes: adding any other interval modality immediately leads to undecidability.
Ichiro Hasuo and Naohiko Hoshino. Semantics of Higher-Order Quantum Computation via Geometry of Interaction
Abstract: Quantum computation attracts growing attention as a new computing
paradigm. While much of its current study employs low-level formalisms
such as quantum circuits, several high-level languages/calculi have
been recently proposed aiming at structured quantum programming. The
current work contributes to the semantical study of such high-level
quantum languages, by providing interaction-based semantics of a
functional quantum programming language---it is based on linear lambda
calculus and equipped with features like the $!$ modality and
recursion.  We prove soundness and adequacy of our semantics. The
construction of our model is by a series of standard techniques taken
from the semantics of classical computation as well as from process
theory, namely: 1) monads with an order structure as models for
branching, used in the coalgebraic study of state-based systems; 2)
Girard's Geometry of Interaction, categorically formulated by
Abramsky, Haghverdi and Scott, providing interaction-based, game-like
semantics for linear logic and computation; and 3) the realizability
technique that turns an (untyped) combinatorial algebra into a
categorical model of a typed calculus. The mathematical genericity of
these techniques---mostly due to their categorical formulation---is
exploited for our move from classical to quantum.
Tomas Brazdil, Vaclav Brozek, Krishnendu Chatterjee, Vojtech Forejt and Antonin Kucera. Two Views on Multiple Mean Payoff Objectives in Markov Decision Processes
Abstract: We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions.
We consider two different objectives, namely, expectation and satisfaction
objectives.
Given an MDP with k reward functions, in the expectation objective the goal is to maximize the expected value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector.
We show that under the expectation objective, in contrast to the single-objective case, both randomization and memory are necessary for strategies, and we show that finite-memory randomized strategies are sufficient. We show that under the satisfaction objective, in contrast to the single-objective case, randomization is necessary for strategies, and we show that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon>0. We show that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon>0.
Our results also reveal flaws in an earlier paper ("Markov Decision Processes with multiple Long-Run Average Objectives", FSTTCS 2007) for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results.
Ugo Dal Lago and Marco Gaboardi. Linear Dependent Types and Relative Completeness
Abstract: A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely capture the functional behaviour of PCF programs (i.e. how the output relates to the input) but also some of their intensional properties, namely the complexity of evaluating them with Krivine Machine. dlPCF is designed around dependent types and linear logic and is parametrized on the underlying language of index terms, which can be tuned so as to sacrifice completeness for decidability.
Separation Logic in the Presence of Garbage Collection
Abstract: Separation logic has proven to be a highly effective tool for the
verification of heap-manipulating programs.  However, it has been
applied almost exclusively in language settings where either memory is
managed manually or the issue of memory management is ignored
altogether.  In this paper, we present a variant of separation logic,
GCSL, for reasoning about low-level programs that interface to a
garbage collector.  In contrast to prior work by Calcagno et al., our
model of GCSL (1) permits reasoning about programs that use internal
pointers and address arithmetic, (2) supports logical variables that
range over pointers, and (3) straightforwardly validates the frame''
rule, as well as a standard interpretation of separation-logic
assertions.  Essential to our approach is the technique (due
originally to McCreight et al.) of distinguishing between logical''
and physical'' states, which enables us to insulate the logic from
the physical reality that pointer values'' may be moved and/or
deallocated by the garbage collector.
Forcing as a program transformation
Abstract: This paper is a study of the forcing translation through the proofs as programs correspondence in classical logic, following the methodology introduced by Krivine in [Kri08,Kri10]. For that, we introduce an extension of (classical) higher-order arithmetic suited to express the forcing translation, called PAw+. We present the proof system of PAw+ - based on Curry-style proof terms with call/cc - as well as the corresponding classical realizability semantics à la Krivine. Then, given a poset of conditions (represented in PAw+ as an upwards closed subset of a fixed meet semi-lattice), we define the forcing translation A -> (p forces A) (where A ranges over propositions) and show that the corresponding transformation of proofs is induced by a simple program transformation t -> t^* defined on raw proof-terms (i.e. independently from the derivation). From an analysis of the computational behavior of transformed programs, we show how to avoid the cost of the transformation by introducing an extension of Krivine's abstract machine devoted to the execution of proofs constructed by forcing. We finally show that this machine induces new classical realizability models and present the corresponding adequacy results.
Ultrametric Semantics of Reactive Programs
Abstract: We describe a denotational model of higher-order functional reactive
programming using ultrametric spaces and nonexpansive maps, which
provides a natural Cartesian closed generalization of causal stream
functions and guarded recursive definitions. We define a type theory
corresponding to this semantics and show that it satisfies
normalization. Finally, we show how reactive programs written in this
language may be implemented efficiently using an imperatively updated
dataflow graph and give a higher-order separation logic proof that
this low-level implementation is correct with respect to the
high-level semantics.
Mikołaj Bojańczyk, Bartek Klin and Sławomir Lasota. Automata with group actions
Abstract: Our motivating question is a Myhill-Nerode theorem for infinite alphabets. We consider several kinds of infinite alphabets:  alphabets whose letters can be compared only for equality, but also alphabets with more structure, such as a total order or a partial order. We develop a framework for studying such alphabets, where the key role is played by the automorphism group of  the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts; nominal sets are  the special case of our framework where letters  can be only compared for equality. We use the  framework to uniformly generalize to infinite alphabets parts of automata theory, including algorithms. In the case of letters compared for equality, we obtain automata equivalent in expressive  power to finite memory automata, as defined by Francez and Kaminski.
The Dichotomy for Conservative Constraint Satisfaction Problems Revisited
Abstract: A central open question in the study of non-uniform constraint satisfaction problems (CSPs) is the dichotomy conjecture of Feder and Vardi stating that the CSP over a fixed constraint language is either NP-complete, or tractable.
One of the main achievements in this direction is a result of Bulatov (LICS'03) confirming the dichotomy conjecture for conservative CSPs, that is, CSPs over constraint languages containing all unary relations.
Unfortunately, the proof is very long and complicated, and therefore hard to understand even for a specialist.
This paper provides a short and transparent proof.
Proof nets for additive linear logic with units
Abstract: Additive linear logic, the fragment of linear logic concerning linear implication between strictly additive formulae, coincides with sum-product logic, the internal language of categories with free finite products and coproducts. Deciding equality of its proof terms, as imposed by the categorical laws, is complicated by the presence of the units (the initial and terminal objects of the category) and the fact that in a free setting products and coproducts do not distribute. The best known desicion algorithm, due to Cockett and Santocanale (CSL 2009), is highly involved, requiring an intricate case analysis on the syntax of terms.

This paper provides canonical, graphical representations of the categorical morphisms, yielding a novel solution to this decision problem. Starting with (a modification of) existing proof nets, due to Hughes and Van Glabbeek, for additive linear logic without units, canonical forms are obtained by graph rewriting. The rewriting algorithm is remarkably simple. As a decision procedure for term equality it matches the known complexity of the problem. A main technical contribution of the paper is the substantial correctness proof of the algorithm.
Bruno Barras, Jean-Pierre Jouannaud, Pierre-Yves Strub and Qian Wang. COQ MTU : a higher-order type theory with a predicative hierachy of universes parameterized by a decidable first-order theory
Abstract: We study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of Universes and a first-order theory T built in its conversion relation. The built-in theory T is specified abstractly, by a set of constructors, a set of defined symbols, axioms expressing that constructors are free and defined symbols completely defined, and a generic elimination principle relying on crucial properties of first-order structures satisfying these axioms. We first show that CoqMTU enjoys the usual meta-theoretical properties of such calculi, including confluence and subject reduction. We then show that predicative beta-reductions enjoy normal forms. This result is then used to build an induction principle in order to show the strong normalization of CoqMTU when restricted to weak-elimination, implying the decidability of type-checking in this case as well as consistency.
Michael Benedikt, Gabriele Puppis and Cristian Riveros. Regular Repair of Specifications
Abstract: What do you do if a computational object (e.g. program trace) fails a specification? An obvious approach is to perform \emph{repair}: modify the object minimally to get something that satisfies the constraints. This approach has been extensively investigated in the database community, for relational integrity constraints, and in the AI community for classical (e.g propositional) logics. In this paper we study it for temporal constraints, given as regular languages or temporal logic formulas. We focus on determining the maximal number of repairs that must be applied to a word satisfying a given input constraint in order to ensure that it satisfies a given target constraint. This maximum may well be infinite; one of our main contributions is to determine when it is finite -- isolating the complexity of the bounded repair problem'', based on a characterization of the pairs of regular languages that admit such a repair. We consider this in the setting where the repair strategy is unconstrained and also when the strategy is restricted to use finite memory. For the latter case, we analyze several models of streaming repair strategies'' (different cost models and lookahead). Although the streaming setting is quite different from the general setting, we find that there are surprising connections between streaming and non-streaming, as well as within variants of the streaming problem.
Benjamin Aminof, Orna Kupferman and Robby Lampert. Rigorous Approximated Determinization of Weighted Automata
Abstract: A {\em nondeterministic weighted finite automaton\/} (WFA) maps an
input word to a numerical value. Applications of weighted
automata include formal verification of quantitative properties, as
well as text, speech, and image processing. Many of these applications
require the WFAs to be deterministic, or work substantially better
when the WFAs are deterministic. Unlike NFAs, which can always be
determinized, not all WFAs have an equivalent deterministic weighted
automaton (DWFA). In \cite{Moh97}, Mohri describes a determinization
construction for a subclass of WFA. He also describes a property of
WFAs (the {\em twins property}), such that all WFA that satisfy the
twins property are determinizable and the algorithm terminates on them.
Unfortunately, many natural WFA do not satisfy the twins property and
cannot be determinized using Mohri's algorithm.

In this paper we study {\em approximated determinization\/} of WFAs.
We describe an algorithm that, given a WFA $\A$ and an
approximation factor $t > 1$, constructs a DWFA $\A'$ that {\em $t$-
determinizes\/} $\A$. Formally,  for all words $w \in \Sigma^*$, the
value of $w$ in $\A'$ is at least its value in $\A$ and at most $t$
times its value in $\A$. Our construction involves two new ideas:
attributing states in the subset construction by both upper and lower
residues, and collapsing attributed subsets whose residues can be
tightened.
The larger the approximation factor is, the more attributed subsets we
can collapse. Thus, $t$-determinization is helpful not only for WFAs that
cannot be determinized, but also in cases determinization is possible
but results in automata that are too big to handle. In addition,
$t$-determinization is useful for reasoning about the competitive
ratio of online algorithms. We also describe a property (the {\em $t$-twins property}) and use it in order to characterize $t$-determinizable WFAs.
Finally, we describe a polynomial algorithm for deciding whether a
given WFA has the $t$-twins property.