IA Scholar Query: The Boolean Closures of the Deterministic and Nondeterministic Context-Free Languages.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 28 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Cost Automata, Safe Schemes, and Downward Closures
https://scholar.archive.org/work/ir2jfld7jrhhno7igngt72hpyy
Higher-order recursion schemes are an expressive formalism used to define languages of finite and infinite ranked trees. They extend regular and context-free grammars, and are equivalent in expressive power to the simply typed λ Y-calculus and collapsible pushdown automata. In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata over infinite trees with a boundedness acceptance condition. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes.David Barozzini, Lorenzo Clemente, Thomas Colcombet, Paweł Paryswork_ir2jfld7jrhhno7igngt72hpyyWed, 28 Sep 2022 00:00:00 GMTConvexity via Weak Distributive Laws
https://scholar.archive.org/work/m4mqnwgeqrf2lkgzd4wdxjtbta
We study the canonical weak distributive law δ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise δ as a convex closure in the free semimodule of a set. Using the abstract theory of weak distributive laws, we compose the powerset and the semimodule monads via δ, obtaining the monad of convex subsets of the free semimodule.Filippo Bonchi, Alessio Santamariawork_m4mqnwgeqrf2lkgzd4wdxjtbtaFri, 23 Sep 2022 00:00:00 GMTParametric Interval Temporal Logic over Infinite Words
https://scholar.archive.org/work/fetbqd5zangcdfhtf74o57ckmi
Model checking for Halpern and Shoham's interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics. Here, we focus on the trace-based semantics, where the infinite execution paths (traces) of the given (finite) Kripke structure are the main semantic entities. In this setting, each finite infix of a trace is interpreted as an interval, and a proposition holds over an interval if and only if it holds over each component state (homogeneity assumption). In this paper, we introduce a quantitative extension of HS over traces, called parametric HS (PHS). The novel logic allows to express parametric timing constraints on the duration (length) of the intervals. We show that checking the existence of a parameter valuation for which a Kripke structure satisfies a PHS formula (model checking), or a PHS formula admits a trace as a model under the homogeneity assumption (satisfiability) is decidable. Moreover, we identify a fragment of PHS which subsumes parametric LTL and for which model checking and satisfiability are shown to be EXPSPACE-complete.Laura Bozzelliwork_fetbqd5zangcdfhtf74o57ckmiWed, 21 Sep 2022 00:00:00 GMTA first-order logic characterization of safety and co-safety languages
https://scholar.archive.org/work/xf3hndravnfbdhn6atzyne46ru
Linear Temporal Logic (LTL) is one of the most popular temporal logics, that comes into play in a variety of branches of computer science. Among the various reasons of its widespread use there are its strong foundational properties: LTL is equivalent to counter-free omega-automata, to star-free omega-regular expressions, and (by Kamp's theorem) to the first-order theory of one successor (S1S[FO]). Safety and co-safety languages, where a finite prefix suffices to establish whether a word does not belong or belongs to the language, respectively, play a crucial role in lowering the complexity of problems like model checking and reactive synthesis for LTL. SafetyLTL (resp., coSafetyLTL) is a fragment of LTL where only universal (resp., existential) temporal modalities are allowed, that recognises safety (resp., co-safety) languages only. The main contribution of this paper is the introduction of a fragment of S1S[FO], called SafetyFO, and of its dual coSafetyFO, which are expressively complete with respect to the LTL-definable safety and co-safety languages. We prove that they exactly characterize SafetyLTL and coSafetyLTL, respectively, a result that joins Kamp's theorem, and provides a clearer view of the characterization of (fragments of) LTL in terms of first-order languages. In addition, it gives a direct, compact, and self-contained proof that any safety language definable in LTL is definable in SafetyLTL as well. As a by-product, we obtain some interesting results on the expressive power of the weak tomorrow operator of SafetyLTL, interpreted over finite and infinite words. Moreover, we prove that, when interpreted over finite words, SafetyLTL (resp. coSafetyLTL) devoid of the tomorrow (resp., weak tomorrow) operator captures the safety (resp., co-safety) fragment of LTL over finite words.Alessandro Cimatti and Luca Geatti and Nicola Gigante and Angelo Montanari and Stefano Tonettawork_xf3hndravnfbdhn6atzyne46ruMon, 19 Sep 2022 00:00:00 GMTHistory-deterministic Parikh Automata
https://scholar.archive.org/work/yaa7unjxabepbphoyn47jfzypa
Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure and some of the algorithmic properties of deterministic automata.Enzo Erlich, Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, Martin Zimmermannwork_yaa7unjxabepbphoyn47jfzypaFri, 16 Sep 2022 00:00:00 GMTA case for DOT: Theoretical Foundations for Objects With Pattern Matching and GADT-style Reasoning
https://scholar.archive.org/work/ll2tdshywzdkdkizvfbpyxqmey
Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic class hierarchies currently results in puzzling type errors in most of these languages. Yet this combination of features occurs naturally in many scenarios, such as when manipulating typed ASTs. To support it properly, compilers needs to implement a form of subtyping reconstruction: the ability to reconstruct subtyping information uncovered at runtime during pattern matching. We introduce cDOT, a new calculus in the family of Dependent Object Types (DOT) intended to serve as a formal foundation for subtyping reconstruction. Being descended from pDOT, itself a formal foundation for Scala, cDOT can be used to encode advanced object-oriented features such as generic inheritance, type constructor variance, F-bounded polymorphism, and first-class recursive modules. We demonstrate that subtyping reconstruction subsumes GADTs by encoding λ_2,Gμ, a classical constraint-based GADT calculus, into cDOT.Aleksander Boruch-Gruszecki, Radosław Waśko, Yichen Xu, Lionel Parreauxwork_ll2tdshywzdkdkizvfbpyxqmeyThu, 15 Sep 2022 00:00:00 GMTOn Feller continuity and full abstraction
https://scholar.archive.org/work/3mxaqxc32zdhxoo4vapqzpe3da
We study the nature of applicative bisimilarity in λ-calculi endowed with operators for sampling from contin- uous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion of Feller-continuity for labelled Markov processes, which we believe of independent interest, giving rise a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound.Gilles Barthe, Raphaëlle Crubillé, Ugo Dal Lago, Francesco Gavazzowork_3mxaqxc32zdhxoo4vapqzpe3daMon, 29 Aug 2022 00:00:00 GMTOn the Generative Capacity of Contextual Grammars with Strictly Locally Testable Selection Languages
https://scholar.archive.org/work/ofcckwcxuzadvca5orc5ejgjfi
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages generated by contextual grammars where all selection languages are elements of a certain subregular language family form again a language family. We investigate contextual grammars with strictly locally testable selection languages and compare those families to families which are based on finite, monoidal, nilpotent, combinational, definite, suffix-closed, ordered, commutative, circular, non-counting, power-separating, or union-free languages.Jürgen Dassow, Bianca Truthework_ofcckwcxuzadvca5orc5ejgjfiSat, 27 Aug 2022 00:00:00 GMTSolving Infinite Games in the Baire Space
https://scholar.archive.org/work/vti3mjlfozffhk2tn2rnlxmteq
Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space ω^ω. We consider such games defined by a natural kind of parity automata over the alphabet ℕ, called ℕ-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical Büchi-Landweber Theorem (for finite-state games in the Cantor space 2^ω) holds again for the present games: A game defined by a deterministic parity ℕ-MSO-automaton is determined, the winner can be computed, and an ℕ-MSO-transducer realizing a winning strategy for the winner can be constructed.Benedikt Brütsch, Wolfgang Thomaswork_vti3mjlfozffhk2tn2rnlxmteqTue, 23 Aug 2022 00:00:00 GMTCountdown μ-Calculus
https://scholar.archive.org/work/prrmbltdpbcyvcwhmh2c52hage
We introduce the countdown μ-calculus, an extension of the modal μ-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties such as the existence of arbitrarily long sequences of specific actions. The standard correspondence with parity games and automata extends to suitably defined countdown games and automata. However, unlike in the classical setting, the scalar fragment is provably weaker than the full vectorial calculus and corresponds to automata satisfying a simple syntactic condition. We establish some facts, in particular decidability of the model checking problem and strictness of the hierarchy induced by the maximal allowed nesting of our new operators.Jędrzej Kołodziejski, Bartek Klin, Stefan Szeider, Robert Ganian, Alexandra Silvawork_prrmbltdpbcyvcwhmh2c52hageMon, 22 Aug 2022 00:00:00 GMTRegular Monoidal Languages
https://scholar.archive.org/work/flo7cywpj5h6hbzgc5cw5a7u6q
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of languages over string diagrams. We use the algebra of monoidal categories to investigate the properties of regular monoidal languages, and provide sufficient conditions for their recognizability by deterministic monoidal automata.Matthew Earnshaw, Paweł Sobociński, Stefan Szeider, Robert Ganian, Alexandra Silvawork_flo7cywpj5h6hbzgc5cw5a7u6qMon, 22 Aug 2022 00:00:00 GMTVerification-Preserving Inlining in Automatic Separation Logic Verifiers (extended version)
https://scholar.archive.org/work/4wiz26i6w5fz3isd3ta7on7omy
Bounded verification has proved useful to detect bugs and to increase confidence in the correctness of a program. In contrast to unbounded verification, reasoning about calls via (bounded) inlining and about loops via (bounded) unrolling does not require method specifications and loop invariants and, therefore, reduces the annotation overhead to the bare minimum, namely specifications of the properties to be verified. For verifiers based on traditional program logics, verification via inlining (and unrolling) is verification-preserving: successful unbounded verification of a program w.r.t. some annotation implies successful verification of the inlined program. That is, any error detected in the inlined program reveals a true error in the original program. However, this essential property might not hold for automatic separation logic verifiers such as Caper, GRASShopper, RefinedC, Steel, VeriFast, and verifiers based on Viper. In this setting, inlining generally changes the resources owned by method executions, which may affect automatic proof search algorithms and introduce spurious errors. In this paper, we present the first technique for verification-preserving inlining in automatic separation logic verifiers. We identify a semantic condition on programs and prove in Isabelle/HOL that it ensures verification-preserving inlining for state-of-the-art automatic separation logic verifiers. We also prove a dual result: successful verification of the inlined program ensures that there are method and loop annotations that enable the verification of the original program for bounded executions. To check our semantic condition automatically, we present two approximations that can be checked syntactically and with a program verifier, respectively. We implemented these checks in Viper and demonstrate that they are effective for non-trivial examples from different verifiers.Thibault Dardinier, Gaurav Parthasarathy, Peter Müllerwork_4wiz26i6w5fz3isd3ta7on7omyMon, 22 Aug 2022 00:00:00 GMTThe Complexity of Iterated Reversible Computation
https://scholar.archive.org/work/44fzi2w5nrbhfng2p6golq3oo4
We study a class of functional problems reducible to computing f^(n)(x) for inputs n and x, where f is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its definition, and in whether we require f to have a polynomial-time inverse or to be computible by a reversible logic circuit. These problems are characterized by the complexity class 𝖥𝖯^𝖯𝖲𝖯𝖠𝖢𝖤, and include natural 𝖥𝖯^𝖯𝖲𝖯𝖠𝖢𝖤-complete problems in circuit complexity, cellular automata, graph algorithms, and the dynamical systems described by piecewise-linear transformations.David Eppsteinwork_44fzi2w5nrbhfng2p6golq3oo4Sun, 21 Aug 2022 00:00:00 GMTExact Separation Logic
https://scholar.archive.org/work/6w47e3etcffhnp3fuvvn4awnqq
Over-approximating (OX) program logics, such as separation logic, are used to verify properties of heap-manipulating programs: all terminating behaviour is characterised but the reported results and errors need not be reachable. OX function specifications are thus incompatible with true bug-finding supported by symbolic execution tools such as Pulse and Gillian. In contrast, under-approximating (UX) program logics, such as incorrectness separation logic, are used to find true results and bugs: reported results and errors are reachable, but not all behaviour can be characterised. UX function specifications thus cannot capture full verification. We introduce exact separation logic (ESL), which provides fully verified function specifications compatible with true bug finding: all terminating behaviour is characterised, and all reported results and errors are reachable. ESL requires subtle definitions of internal and external function specifications compared with the familiar definitions of OX logics. It supports reasoning about mutually recursive functions and non-termination. We prove frame-preserving soundness for ESL, demonstrating, for the first time, functional compositionality for a non-OX program logic. We investigate the expressivity of ESL and the role of abstraction in UX reasoning by verifying abstract ESL specifications of list algorithms. To show overall viability of exact verification for true bug-finding, we formalise a compositional symbolic execution semantics capable of using ESL specifications and characterise the conditions that these specifications must respect so that true bug-finding is preserved.Petar Maksimović and Caroline Cronjäger and Julian Sutherland and Andreas Lööw and Sacha-Élie Ayoun and Philippa Gardnerwork_6w47e3etcffhnp3fuvvn4awnqqTue, 16 Aug 2022 00:00:00 GMTOn the Expressiveness of Mixed Choice Sessions (Technical Report)
https://scholar.archive.org/work/fkrin2m4kbdsvgnjrla7kjff7m
Session types provide a flexible programming style for structuring interaction, and are used to guarantee a safe and consistent composition of distributed processes. Traditional session types include only one-directional input (external) and output (internal) guarded choices. This prevents the session-processes to explore the full expressive power of the pi-calculus where the mixed choices are proved more expressive than the (non-mixed) guarded choices. To account this issue, recently Casal, Mordido, and Vasconcelos proposed the binary session types with mixed choices (CMV+). This paper carries a surprising, unfortunate result on CMV+: in spite of an inclusion of unrestricted channels with mixed choice, CMV+'s mixed choice is rather separate and not mixed. We prove this negative result using two methodologies (using either the leader election problem or a synchronisation pattern as distinguishing feature), showing that there exists no good encoding from the pi-calculus into CMV+, preserving distribution. We then close their open problem on the encoding from CMV+ into CMV (without mixed choice), proving its soundness and thereby that the encoding is good up to coupled similarity. This technical report extends a paper presented at the workshop EXPRESS/SOS'22.Kirstin Peters, Nobuko Yoshidawork_fkrin2m4kbdsvgnjrla7kjff7mMon, 15 Aug 2022 00:00:00 GMTQuasilinear-time Computation of Generic Modal Witnesses for Behavioural Inequivalence
https://scholar.archive.org/work/ye5b3kh5yrc7tdzazu5w4dzr7m
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the paradigm of universal coalgebra. For every behavioural equivalence class in a given system, we construct a formula which holds precisely at the states in that class. The algorithm instantiates to deterministic finite automata, transition systems, labelled Markov chains, and systems of many other types. The ambient logic is a modal logic featuring modalities that are generically extracted from the functor; these modalities can be systematically translated into custom sets of modalities in a postprocessing step. The new algorithm builds on an existing coalgebraic partition refinement algorithm. It runs in time 𝒪((m+n) log n) on systems with n states and m transitions, and the same asymptotic bound applies to the dag size of the formulae it constructs. This improves the bounds on run time and formula size compared to previous algorithms even for previously known specific instances, viz. transition systems and Markov chains; in particular, the best previous bound for transition systems was 𝒪(m n).Thorsten Wißmann, Stefan Milius, Lutz Schröderwork_ye5b3kh5yrc7tdzazu5w4dzr7mMon, 15 Aug 2022 00:00:00 GMTSimulation by Rounds of Letter-to-Letter Transducers
https://scholar.archive.org/work/r5ma34hukvevdla3noaywohpqe
Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output letters within "rounds". In this work, we introduce and study notions of simulation by rounds and equivalence by rounds of transducers. In our setting, words are partitioned to consecutive subwords of a fixed length k, called rounds. Then, a transducer 𝒯_1 is k-round simulated by transducer 𝒯_2 if, intuitively, for every input word x, we can permute the letters within each round in x, such that the output of 𝒯_2 on the permuted word is itself a permutation of the output of 𝒯_1 on x. Finally, two transducers are k-round equivalent if they simulate each other. We solve two main decision problems, namely whether 𝒯_2 k-round simulates 𝒯_1 (1) when k is given as input, and (2) for an existentially quantified k. We demonstrate the usefulness of the definitions by applying them to process symmetry: a setting in which a permutation in the identities of processes in a multi-process system naturally gives rise to two transducers, whose k-round equivalence corresponds to stability against such permutations.Antonio Abu Nassar, Shaull Almagorwork_r5ma34hukvevdla3noaywohpqeSun, 14 Aug 2022 00:00:00 GMTAll about unambiguous polynomial closure
https://scholar.archive.org/work/umdpibpkrvddpeculi22og5kre
We investigate a standard operator on classes of languages: unambiguous polynomial closure. We prove that for every class C of regular languages satisfying mild properties, the membership problem for its unambiguous polynomial closure UPol(C) reduces to the same problem for C. We also show that unambiguous polynomial closure coincides with alternating left and right deterministic closure. Moreover, we prove that if additionally C is finite, the separation and covering problems are decidable for UPol(C). Finally, we present an overview of the generic logical characterizations of the classes built using unambiguous polynomial closure.Thomas Place, Marc Zeitounwork_umdpibpkrvddpeculi22og5kreSun, 14 Aug 2022 00:00:00 GMTCo-lexicographically ordering automata and regular languages. Part I
https://scholar.archive.org/work/rvvbtgysgjd3rpxubqb2idhigi
In the present work, we lay out a new theory showing that all automata can always be co-lexicographically partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width p of one of their admissible co-lex partial orders - dubbed here the automaton's co-lex width. We first show that this new measure captures at once the complexity of several seemingly-unrelated hard problems on automata. Any NFA of co-lex width p: (i) has an equivalent powerset DFA whose size is exponential in p rather than (as a classic analysis shows) in the NFA's size; (ii) can be encoded using just Θ(log p) bits per transition; (iii) admits a linear-space data structure solving regular expression matching queries in time proportional to p^2 per matched character. Some consequences of this new parameterization of automata are that PSPACE-hard problems such as NFA equivalence are FPT in p, and quadratic lower bounds for the regular expression matching problem do not hold for sufficiently small p. Having established that the co-lex width of an automaton is a fundamental complexity measure, we proceed by (i) determining its computational complexity and (ii) extending this notion from automata to regular languages by studying their smallest-width accepting NFAs and DFAs. In this work we focus on the deterministic case and prove that a canonical minimum-width DFA accepting a language ℒ - dubbed the Hasse automaton ℋ of ℒ - can be exhibited. Finally, we explore the relationship between two conflicting objectives: minimizing the width and minimizing the number of states of a DFA. In this context, we provide an analogous of the Myhill-Nerode Theorem for co-lexicographically ordered regular languages.Nicola Cotumaccio, Giovanna D'Agostino, Alberto Policriti, Nicola Prezzawork_rvvbtgysgjd3rpxubqb2idhigiTue, 09 Aug 2022 00:00:00 GMTMSO Queries on Trees: Enumerating Answers under Updates Using Forest Algebras
https://scholar.archive.org/work/2o5hy6mo7ves3n6wlxm5v2c5wi
We describe a framework for maintaining forest algebra representations of trees of logarithmic height. Such a representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential interest for data structures and algorithms for trees whose complexity depend on the depth of the tree (representation). We provide an exemplary application of the framework to the problem of efficiently enumerating answers to MSO-definable queries over trees which are subject to local updates. We exhibit an algorithm that uses an O(n) preprocessing phase and enumerates answers with O(log(n)) delay between them. When the tree is updated, the algorithm can avoid repeating expensive preprocessing and restart the enumeration phase within O(log(n)) time. Our algorithms and complexity results in the paper are presented in terms of node-selecting tree automata representing the MSO queries.Sarah Kleest-Meißner, Jonas Marasus, Matthias Niewerthwork_2o5hy6mo7ves3n6wlxm5v2c5wiMon, 08 Aug 2022 00:00:00 GMT