Cost Automata, Safe Schemes, and Downward Closures

Barozzini, David; Clemente, Lorenzo; Colcombet, Thomas; Parys, Paweł

doi:10.4230/lipics.icalp.2020.109

Cited by 3 publications

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“…The domain of a decision function y for a decision pP, X pkq q allowing the player P to choose x pkq P X pkq is the product of V , M , and all the possible previous sets of possible options of the opponent in a round. The range of y is Y , with the restriction that the player P needs to preserve the invariant as in (1).…”

Section: Gamesmentioning

confidence: 99%

“…Related works. Over finite words, variants of the pC, Dq-separability problem have been studied for classes C both more general than the regular languages, such as the context free languages [22,49] and higher-order languages [14] (later extended to safe schemes over finite trees [1]), and for classes D more restrictive than the regular languages, such as in [39,40]. The separability and membership problems have also been studied for several classes of infinite-state systems, such as vector addition systems [11,10,23], well-structured transition systems [21], one-counter automata [20], and timed automata [13,12].…”

Section: Introductionmentioning

confidence: 99%

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Deterministic and game separability for regular languages of infinite trees

Clemente,

Skrzypczak

2021

Preprint

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We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the separator is fixed, or not. In each case, we show that separability can be decided in EXPTIME, and that separating automata of exponential size suffice. We obtain our results by reducing to infinite duration games with ω-regular winning conditions and applying the finite-memory determinacy theorem of Büchi and Landweber.

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Section: Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deterministic and game separability for regular languages of infinite trees

Clemente,

Skrzypczak

2021

Preprint

Self Cite

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Unboundedness Problems for Machines with Reversal-Bounded Counters

Baumann

D'Alessandro

Ganardi

et al. 2023

Lecture Notes in Computer Science

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We consider a general class of decision problems concerning formal languages, called “(one-dimensional) unboundedness predicates”, for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces—non-deterministically in polynomial time—to the same problem for just finite automata. We also show an analogous reduction for automata that have access to both a pushdown stack and reversal-bounded counters (PRBCA).This allows us to answer several open questions: For example, we show that it is $$\textsf{coNP}$$ coNP -complete to decide whether a given (P)RBCA language L is bounded, meaning whether there exist words $$w_1,\ldots ,w_n$$ w 1 , … , w n with $$L\subseteq w_1^*\cdots w_n^*$$ L ⊆ w 1 ∗ ⋯ w n ∗ . For PRBCA, even decidability was open. Our methods also show that there is no language of a (P)RBCA of intermediate growth. This means, the number of words of each length grows either polynomially or exponentially. Part of our proof is likely of independent interest: We show that one can translate an RBCA into a machine with $$\mathbb {Z}$$ Z -counters in logarithmic space, while preserving the accepted language.

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Existential Definability over the Subword Ordering

Baumann,

Ganardi,

Thinniyam

et al. 2022

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Cost Automata, Safe Schemes, and Downward Closures

Cited by 3 publications

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Deterministic and game separability for regular languages of infinite trees

Deterministic and game separability for regular languages of infinite trees

Unboundedness Problems for Machines with Reversal-Bounded Counters

Existential Definability over the Subword Ordering

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