Alternation Elimination by Complementation (Extended Abstract)

Dax, Christian; Klaedtke, Felix

doi:10.1007/978-3-540-89439-1_16

Cited by 18 publications

(29 citation statements)

References 23 publications

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“…In particular, the ns from condition (6) mark the end positions of the segments in the splitting. We remark that we have given in [11] a similar characterization for word automata. The main differences to nested words are as follows.…”

Section: Complementing Existential Co-büchi Automatamentioning

confidence: 69%

“…In this section, we generalize our alternation-elimination scheme for word automata, which we presented in [11], to automata that operate over graphs.…”

Section: Alternation-elimination Schemementioning

confidence: 99%

“…We now turn to the construction of the NWA, which generalizes our construction in [11] for complementing the word language of an eventually {1}-way ECA, which in turn on is based on the breakpoint construction [16]. The additional constraints for the non-local moves in the conditions (2), (5), and (6) are handled by using the stack of the NWA.…”

Section: Complementing Existential Co-büchi Automatamentioning

confidence: 99%

“…We obtain the alternation-elimination constructions for automata that describe nested-word languages from a construction scheme, which we previously presented for word automata [11] and which we generalize in this paper to automata that operate over the tree unfolding of graphs. In a nutshell, the construction scheme shows that the problem of translating an alternating automaton into a nondeterministic automaton reduces to the problem of complementing an existential automaton, i.e., an automaton that nondeterministically inspects only a single branch in the tree unfolding of the given input graph.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, ingredients of the presented constructions are based on existing well established and thoroughly optimized constructions and techniques for nondeterministic word automata, which we generalize to automata that operate over the tree unfolding of the graphs given by nested words. First, we extend our complementation constructions for classes of nondeterministic two-way coBüchi word automata [11] to classes of existential co-Büchi automata, where the inputs are the graphs of nested words. Our new constructions take the non-local transitions, which stem from the hierarchical structure of nested words, of an existential automaton into account.…”

Section: Introductionmentioning

confidence: 99%

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Alternation Elimination for Automata over Nested Words

Dax

Klaedtke

2011

Foundations of Software Science and Computational Structures

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Abstract. This paper presents constructions for translating alternating automata into nondeterministic nested-word automata (NWAs). With these alternation-elimination constructions at hand, we straightforwardly obtain translations from various temporal logics over nested words from the literature like CaRet and μNWTL, and extensions thereof to NWAs, which correct, simplify, improve, and generalize the previously given translations. Our alternation-elimination constructions are instances of an alternation-elimination scheme for automata that operate over the tree unfolding of graphs. We obtain these instances by providing constructions for complementing restricted classes of automata with respect to the graphs given by nested words. The scheme generalizes our alternation-elimination scheme for word automata and the presented complementation constructions generalize existing complementation constructions for word automata.

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Section: Complementing Existential Co-büchi Automatamentioning

confidence: 69%

“…In this section, we generalize our alternation-elimination scheme for word automata, which we presented in [11], to automata that operate over graphs.…”

Section: Alternation-elimination Schemementioning

confidence: 99%

Section: Complementing Existential Co-büchi Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Alternation Elimination for Automata over Nested Words

Dax

Klaedtke

2011

Foundations of Software Science and Computational Structures

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Model Checking Branching Properties on Petri Nets with Transits

Finkbeiner

Gieseking

Hecking-Harbusch

et al. 2020

Automated Technology for Verification and Analysis

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On Regular Temporal Logics with Past,

Dax

Klaedtke

Lange

2009

Automata, Languages and Programming

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The IEEE standardized Property Specification Language, PSL for short, extends the well-known linear-time temporal logic LTL with so-called semi-extended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the hardware design cycle, from specification to verification. In this article, we extend the common core of these specification languages with past operators. We name this extension PPSL. Although all ω-regular properties are expressible in PSL, SVA, and PPSL, past operators often allow one to specify properties more naturally and concisely. In fact, we show that PPSL is exponentially more succinct than the cores of PSL and SVA. On the star-free properties, PPSL is double exponentially more succinct than LTL. Furthermore, we present a translation of PPSL into language-equivalent nondeterministic Büchi automata, which is based on novel constructions for 2-way alternating automata. The upper bound on the size of the resulting nondeterministic Büchi automata obtained by our translation is almost the same as the upper bound for the nondeterministic Büchi automata obtained from existing translations for PSL and SVA. Consequently, the satisfiability problem and the model-checking problem for PPSL fall into the same complexity classes as the corresponding problems for PSL and SVA.

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Alternation Elimination by Complementation (Extended Abstract)

Cited by 18 publications

References 23 publications

Alternation Elimination for Automata over Nested Words

Alternation Elimination for Automata over Nested Words

Model Checking Branching Properties on Petri Nets with Transits

On Regular Temporal Logics with Past,

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