103 research outputs found

    The Containment Problem for Unambiguous Register Automata

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    We investigate the complexity of the containment problem "Does L(A)subseteq L(B) hold?", where B is an unambiguous register automaton and A is an arbitrary register automaton. We prove that the problem is decidable and give upper bounds on the computational complexity in the general case, and when B is restricted to have a fixed number of registers

    Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata

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    We study the universality and inclusion problems for register automata over equality data. We show that the universality and the inclusion problems can be solved with 2-EXPTIME complexity when the input automata are without guessing and unambiguous, improving on the currently best-known 2-EXPSPACE upper bound by Mottet and Quaas. When the number of registers of both automata is fixed, we obtain a lower EXPTIME complexity, also improving the EXPSPACE upper bound from Mottet and Quaas for fixed number of registers. We reduce inclusion to universality, and then we reduce universality to the problem of counting the number of orbits of runs of the automaton. We show that the orbit-counting function satisfies a system of bidimensional linear recursive equations with polynomial coefficients (linrec), which generalises analogous recurrences for the Stirling numbers of the second kind, and then we show that universality reduces to the zeroness problem for linrec sequences. While such a counting approach is classical and has successfully been applied to unambiguous finite automata and grammars over finite alphabets, its application to register automata over infinite alphabets is novel. We provide two algorithms to decide the zeroness problem for bidimensional linear recursive sequences arising from orbit-counting functions. Both algorithms rely on techniques from linear non-commutative algebra. The first algorithm performs variable elimination and has elementary complexity. The second algorithm is a refined version of the first one and it relies on the computation of the Hermite normal form of matrices over a skew polynomial field. The second algorithm yields an EXPTIME decision procedure for the zeroness problem of linrec sequences, which in turn yields the claimed bounds for the universality and inclusion problems of register automata.Comment: full version of the homonymous paper to appear in the proceedings of STACS'2

    Language Inclusion for Boundedly-Ambiguous Vector Addition Systems Is Decidable

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    We consider the problems of language inclusion and language equivalence for Vector Addition Systems with States (VASSes) with the acceptance condition defined by the set of accepting states (and more generally by some upward-closed conditions). In general the problem of language equivalence is undecidable even for one-dimensional VASSes, thus to get decidability we investigate restricted subclasses. On one hand we show that the problem of language inclusion of a VASS in k-ambiguous VASS (for any natural k) is decidable and even in Ackermann. On the other hand we prove that the language equivalence problem is Ackermann-hard already for deterministic VASSes. These two results imply Ackermann-completeness for language inclusion and equivalence in several possible restrictions. Some of our techniques can be also applied in much broader generality in infinite-state systems, namely for some subclass of well-structured transition systems

    A Linear-Time Nominal ?-Calculus with Name Allocation

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    Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as nondetermininistic orbit-finite automata (NOFAs), where names play the role of data. Reasoning problems in such formalisms tend to be computationally hard. Name-binding nominal automata models such as {regular nondeterministic nominal automata (RNNAs)} have been shown to be computationally more tractable. In the present paper, we introduce a linear-time fixpoint logic Bar-?TL} for finite words over an infinite alphabet, which features full negation and freeze quantification via name binding. We show by a nontrivial reduction to extended regular nondeterministic nominal automata that even though Bar-?TL} allows unrestricted nondeterminism and unboundedly many registers, model checking Bar-?TL} over RNNAs and satisfiability checking both have elementary complexity. For example, model checking is in 2ExpSpace, more precisely in parametrized ExpSpace, effectively with the number of registers as the parameter

    The many facets of string transducers

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    Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem

    Equivalence of finite-valued streaming string transducers is decidable

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    In this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable

    Logics with rigidly guarded data tests

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    The notion of orbit finite data monoid was recently introduced by Bojanczyk as an algebraic object for defining recognizable languages of data words. Following Buchi's approach, we introduce a variant of monadic second-order logic with data equality tests that captures precisely the data languages recognizable by orbit finite data monoids. We also establish, following this time the approach of Schutzenberger, McNaughton and Papert, that the first-order fragment of this logic defines exactly the data languages recognizable by aperiodic orbit finite data monoids. Finally, we consider another variant of the logic that can be interpreted over generic structures with data. The data languages defined in this variant are also recognized by unambiguous finite memory automata

    36th International Symposium on Theoretical Aspects of Computer Science: STACS 2019, March 13-16, 2019, Berlin, Germany

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