The Model Checking Problem for Prefix Classes of Second-Order Logic: A Survey

Eiter, Thomas; Gottlob, Georg; Schwentick, Thomas

doi:10.1007/978-3-642-15025-8_13

Cited by 3 publications

(2 citation statements)

References 37 publications

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“…Furthermore, for each k 0, the fragments Σ 1 k (∀) and Σ 1 k (∃) only define regular languages. For more information on this topic, the reader is invited to read the beautiful survey of Eiter, Gottlob and Schwentick [19].…”

Section: Logic On Wordsmentioning

confidence: 99%

How to Prove that a Language Is Regular or Star-Free?

2020

Language and Automata Theory and Applications

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This survey article presents some standard and less standard methods used to prove that a language is regular or star-free.Most books of automata theory [9,23,29,46,50] offer exercises on regular languages, including some difficult ones. Further examples can be found on the web sites math.stackexchange.com and cs.stackexchange.com. Another good source of tough questions is the recent book 200 Problems in Formal Languages and Automata Theory [37]. Surprisingly, there is hardly any exercise to prove that a language is star-free. In this paper, we present various methods to prove that a language is regular or star-free.

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Section: Logic On Wordsmentioning

confidence: 99%

How to Prove that a Language Is Regular or Star-Free?

2020

Language and Automata Theory and Applications

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“…In [7], a similar systematical analysis of relational ESO on string structures has been carried out, showing the surprising dichotomy that prefix fragments either fall in REG or they express NP-complete problems (the result is remarkable because it is known that REG is a small class, REG ⊂ NP). In general, see [8] for an overview of the results on relation ESO (up to 2010). For what regards functional ESO, prefix classes seem to be of lesser interest, since it is known ( [15]) that the minimal interesting prefix, ∃f ∀x, already allows expressing NPcomplete problems.…”

Section: Introductionmentioning

confidence: 99%

Complexity of syntactical tree fragments of Independence-Friendly logic

Barbero¹

2016

Preprint

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In 1986 ([2]), Blass and Gurevich proved that any non-linear Henkin quantifier can be applied to a quantifier-free first-order formula in such a way that the resulting sentence characterizes an NP-complete problem. In 2014 Sevenster ([31]) proved a more general result for regular quantifier prefixes of Independence-Friendly (IF ) logic; he showed that these prefixes can express (in the sense described above) either 1) only FO problems or 2) also NP-complete problems. The latter class is constituted by 2a) prefixes that mimic non-linear Henkin quantifiers, and 2b) prefixes that encode game-theoretical phenomena of signalling. Furthermore, the dichotomy result yielded a new sufficient (and recursive) criterion for recognizing IF sentences that are equivalent to first-order sentences.In the present paper we develop the machinery which is needed in order to extend the results of Sevenster to non-prenex (regular) IF sentences. This involves shifting attention from quantifier prefixes to a (rather general) class of synctactical trees. Instrumentally, we explicitate and prove a number of equivalence rules for incomplete synctactical trees.We partially classify the fragments of IF logic that are thus determined by synctactical trees; in particular, we identify three synctactical structures that are neither signalling nor Henkin, and yet express concepts that are beyond the reach of first-order logic.

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The role of model checking in software engineering

Karna

Chen

et al. 2018

Front. Comput. Sci.

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The Model Checking Problem for Prefix Classes of Second-Order Logic: A Survey

Cited by 3 publications

References 37 publications

How to Prove that a Language Is Regular or Star-Free?

How to Prove that a Language Is Regular or Star-Free?

Complexity of syntactical tree fragments of Independence-Friendly logic

The role of model checking in software engineering

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