Nested antichains for WS1S

Fiedor, Tomáš; Holík, Lukáš; Lengál, Ondřej; Vojnar, Tomáš

doi:10.1007/s00236-018-0331-z

Cited by 4 publications

(6 citation statements)

References 22 publications

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“…Although there have recently appeared new techniques for deciding WSkS, e.g. [20,19,24,14,44,21], we do not focus on comparing with them because the alternative tools are far less mature than Mona. Although they can win over Mona on limited classes of formulae, from our experience, Mona performs better overall and, up to our knowledge, can still be considered the only robust and practically usable tool.…”

Section: Discussionmentioning

confidence: 99%

“…We have evaluated our technique on formulae we were able to find in the literature or obtain by personal communication (in cases where the appropriate research was not published due to problems with the scalability of Mona) and which our tool could parse. Particularly, our benchmark includes formulae from the Strand benchmark [31], formulae from the authors of Mona [29], benchmarks for synthesis of regular specifications [23], families of parametric WS1S formulae [20], LTL formulae from [48] translated to the MSO(Str) 7 logic [18], and an experimental translation of separation logic formulae into MSO(Str) [6]. In total, our benchmark set has 103 formulae (95 WS1S and 8 WS2S), available in the tool's repository.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, several works on lazy approaches to the automata decision procedure appeared, namely our works [24,19,20] and a similarly focused work [44]. The idea behind these approaches is that, instead of constructing automata explicitly, they work with an implicit transition relation, which is defined inductively to the structure of a formula.…”

Section: Related Workmentioning

confidence: 99%

“…In practice, however, Mona is still substantially most robust by a large margin (partially owing to the relative immaturity of the alternative tools). Variants of our antiprenexing techniques would certainly be relevant for the lazy automata approaches [24,19,20,44]. In [19,20], we have actually successfully used a simple variant of antiprenexing (namely the quantifier distribution rule (QuantDistr)).…”

Section: Related Workmentioning

confidence: 99%

“…Although there have appeared several newer approaches and prototype tools that may beat Mona on restricted sets of formulae [43,32,44,21], including our own approaches [19,20,24],…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Antiprenexing for WSkS: A Little Goes a Long Way

Havlena¹,

Holík²,

Lengál³

et al.

EPiC Series in Computing

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We study light-weight techniques for preprocessing of WSkS formulae in an automata- based decision procedure as implemented, e.g., in Mona. The techniques we use are based on antiprenexing, i.e., pushing quantifiers deeper into a formula. Intuitively, this tries to alleviate the explosion in the size of the constructed automata by making it happen sooner on smaller automata (and have the automata minimization reduce the output). The formula transformations that we use to implement antiprenexing may, however, be applied in different ways and extent and, if used in an unsuitable way, may also cause an explosion in the size of the formula and the automata built while deciding it. Therefore, our approach uses informed rules that use an estimation of the cost of constructing automata for WSkS formulae. The estimation is based on a model learnt from runs of the decision algorithm on various formulae. An experimental evaluation of our technique shows that antiprenexing can significantly boost the performance of the base WSkS decision procedure, sometimes allowing one to decide formulae that could not be decided before.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…Although there have appeared several newer approaches and prototype tools that may beat Mona on restricted sets of formulae [43,32,44,21], including our own approaches [19,20,24],…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Antiprenexing for WSkS: A Little Goes a Long Way

Havlena¹,

Holík²,

Lengál³

et al.

EPiC Series in Computing

View full text Add to dashboard Cite

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Language Inclusion Algorithms as Complete Abstract Interpretations

2019

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We study the language inclusion problem L1 ⊆ L2 where L1 is regular. Our approach relies on abstract interpretation and checks whether an overapproximating abstraction of L1, obtained by successively overapproximating the Kleene iterates of its least fixpoint characterization, is included in L2. We show that a language inclusion problem is decidable whenever this overapproximating abstraction satisfies a completeness condition (i.e. its loss of precision causes no false alarm) and prevents infinite ascending chains (i.e. it guarantees termination of least fixpoint computations). Such overapproximating abstraction function on languages can be defined using quasiorder relations on words where the abstraction gives the language of all words "greater than or equal to" a given input word for that quasiorder. We put forward a range of quasiorders that allow us to systematically design decision procedures for different language inclusion problems such as regular languages into regular languages or into trace sets of one-counter nets. In the case of inclusion between regular languages, some of the induced inclusion checking procedures correspond to well-known state-of-the-art algorithms like the so-called antichain algorithms. Finally, we provide an equivalent greatest fixpoint language inclusion check which relies on quotients of languages and, to the best of our knowledge, was not previously known.

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Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic

Habermehl,

Havlena,

Hečko

et al. 2024

Computer Aided Verification

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We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work directly with numbers. This combination is enabled by a fine-grained version of the duality between automata and arithmetic formulae. In particular, we employ a construction where states of automaton are obtained as derivatives of arithmetic formulae: then every state corresponds to a formula. Optimizations based on techniques and ideas transferred from the world of algebraic methods are used on thousands of automata states, which dramatically amplifies their effect. The merit of this combination of automata with algebraic methods is demonstrated by our prototype implementation being competitive to and even superior to state-of-the-art SMT solvers.

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Nested antichains for WS1S

Cited by 4 publications

References 22 publications

Antiprenexing for WSkS: A Little Goes a Long Way

Antiprenexing for WSkS: A Little Goes a Long Way

Language Inclusion Algorithms as Complete Abstract Interpretations

Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic

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