On the separability of sparse context-free languages and of bounded rational relations

Choffrut, Christian; D'Alessandro, Flavio; Varricchio, Stefano

doi:10.1016/j.tcs.2007.04.003

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…These applications justify a systematic study of the separation problem. It is therefore surprising that it deserved only little attention and isolated work [9,10,41,19], even in the restricted, yet still challenging case of regular languages.…”

Section: Introductionmentioning

confidence: 99%

On Separation by Locally Testable and Locally Threshold Testable Languages

Place¹,

Rooijen²,

Zeitoun³

2014

Logical Methods in Computer Science

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Abstract. A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting the input languages. We prove that the problem is computationally harder than deciding membership. The correctness proof of the algorithm yields a stronger result, namely a description of a possible separator. Finally, we discuss the same problem for context-free input languages.

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Section: Introductionmentioning

confidence: 99%

On Separation by Locally Testable and Locally Threshold Testable Languages

Place¹,

Rooijen²,

Zeitoun³

2014

Logical Methods in Computer Science

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“…If the input languages are themselves regular and S is a subclass [42,41,40,39,43,44,35,15], then separability generalizes the classical subclass membership problem. Moreover, separability for languages of infinite-state systems has received a significant amount of attention [17,16,14,13,10,9,12,1,51,48,11,8]. Let us point out two prominent cases.…”

Section: Introductionmentioning

confidence: 99%

Regular Separability in Büchi VASS

Baumann¹,

Meyer²,

Zetzsche³

2023

Preprint

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We study the (ω-)regular separability problem for Büchi VASS languages: Given two Büchi VASS with languages L1 and L2, check whether there is a regular language that fully contains L1 while remaining disjoint from L2. We show that the problem is decidable in general and PSPACE-complete in the 1-dimensional case, assuming succinct counter updates. The results rely on several arguments. We characterize the set of all regular languages disjoint from L2. Based on this, we derive a (sound and complete) notion of inseparability witnesses, non-regular subsets of L1. Finally, we show how to symbolically represent inseparability witnesses and how to check their existence.

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“…The separation problem appears in many disciplines of mathematics and computer science, such as algebra [3,4,22], logic [24,25], formal languages [7,23], learning theory [16], and recently also in databases and query answering [8]. The latter topic is our original motivation we have investigated since the work of [8].…”

Section: Introductionmentioning

confidence: 99%

Alternating Towers and Piecewise Testable Separators

Holub¹,

Masopust²,

Thomazo³

2014

Preprint

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Two languages are separable by a piecewise testable language if and only if there exists no infinite tower between them. An infinite tower is an infinite sequence of strings alternating between the two languages such that every string is a subsequence (scattered substring) of all the strings that follow. For regular languages represented by nondeterministic finite automata, the existence of an infinite tower is decidable in polynomial time. In this paper, we investigate the complexity of a particular method to compute a piecewise testable separator. We show that it is closely related to the height of maximal finite towers, and provide the upper and lower bounds with respect to the size of the given nondeterministic automata. Specifically, we show that the upper bound is polynomial with respect to the number of states with the cardinality of the alphabet in the exponent. Concerning the lower bound, we show that towers of exponential height with respect to the cardinality of the alphabet exist. Since these towers mostly turn out to be sequences of prefixes, we also provide a comparison with towers of prefixes.

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On the separability of sparse context-free languages and of bounded rational relations

Cited by 5 publications

References 13 publications

On Separation by Locally Testable and Locally Threshold Testable Languages

On Separation by Locally Testable and Locally Threshold Testable Languages

Regular Separability in Büchi VASS

Alternating Towers and Piecewise Testable Separators

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