Classifying regular events in symbolic logic

Thomas, Wolfgang

doi:10.1016/0022-0000(82)90016-2

Cited by 256 publications

(184 citation statements)

References 9 publications

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“…Thomas [22] characterizes FO(+1) in terms of Local Threshold Testability, equivalence in terms of the multiplicity of k-factors up to some fixed finite threshold t.…”

Section: Fo(+1)-locally Threshold Testable Languagesmentioning

confidence: 99%

Cognitive and Sub-regular Complexity

et al. 2013

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Abstract. We present a measure of cognitive complexity for subclasses of the regular languages that is based on model-theoretic complexity rather than on description length of particular classes of grammars or automata. Unlike description length approaches, this complexity measure is independent of the implementation details of the cognitive mechanism. Hence, it provides a basis for making inferences about cognitive mechanisms that are valid regardless of how those mechanisms are actually realized.

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“…Thomas [22] characterizes FO(+1) in terms of Local Threshold Testability, equivalence in terms of the multiplicity of k-factors up to some fixed finite threshold t.…”

Section: Fo(+1)-locally Threshold Testable Languagesmentioning

confidence: 99%

Cognitive and Sub-regular Complexity

et al. 2013

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“…In the domain of words, we see that a language is FO S]-de nable i it is locally threshold testable ( Th82a]). The locally threshold testable word languages are usually introduced in a slightly di erent but equivalent w ay than above.…”

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confidence: 97%

Languages, Automata, and Logic

Thomas¹

1997

Handbook of Formal Languages

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733

601

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This paper is a survey on logical aspects of nite automata. Central points are the connection between nite automata and monadic second-order logic, the Ehrenfeucht-Fra ss e t e c hnique in the context of formal language theory, nite automata on !-words and their determinization, and a self-contained proof of the \Rabin Tree Theorem".Sections 5 and 6 contain material presented in a lecture series to the \Final Winter School of AMICS" (Palermo, February 1996). A modi ed version of the paper will be a chapter of the \Handbook of Formal Language Theory", edited by G. Rozenberg and A. Salomaa, to appear in Springer-Verlag.

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“…A different way to view the expressive power of a logic is to identify which regular languages it is capable of defining. It is known that MFOL[<] (equivalently, SDoO) is capable of defining precisely the star-free regular languages [12] and we have recently shown that MFOL[=] (equivalently SD) is capable of defining precisely the commutative star-free regular languages [15] (a language is commutative if it is closed under permutation). Thus, the table 4b can be rewritten in terms of expressiveness as compared to regular languages, where ⊤ defines Σ * and ⊥ defines ∅ (the empty language).…”

Section: Removing Logical Operatorsmentioning

confidence: 99%

Fragments of Spider Diagrams of Order and Their Relative Expressiveness

Delaney

Taylor

Thompson

2010

Diagrammatic Representation and Inference

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Abstract. Investigating the expressiveness of a diagrammatic logic provides insight into how its syntactic elements interact at the semantic level. Moreover, it allows for comparisons with other notations. Various expressiveness results for diagrammatic logics are known, such as the theorem that Shin's Venn-II system is equivalent to monadic first order logic. The techniques employed by Shin for Venn-II were adapted to allow the expressiveness of Euler diagrams to be investigated. We consider the expressiveness of spider diagrams of order (SDoO), which extend spider diagrams by including syntax that provides ordering information between elements. Fragments of SDoO are created by systematically removing each aspect of the syntax. We establish the relative expressiveness of the various fragments. In particular, one result establishes that spiders are syntactic sugar in any fragment that contains order, negation and shading. We also show that shading is syntactic sugar in any fragment containing negation and spiders. The existence of syntactic redundancy within the spider diagram of order logic is unsurprising however, we find it interesting that spiders or shading are redundant in fragments of the logic. Further expressiveness results are presented throughout the paper. The techniques we employ may well extend to related notations, such as the Euler/Venn logic of Swoboda et al. and Kent's constraint diagrams.

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Classifying regular events in symbolic logic

Cited by 256 publications

References 9 publications

Cognitive and Sub-regular Complexity

Cognitive and Sub-regular Complexity

Languages, Automata, and Logic

Fragments of Spider Diagrams of Order and Their Relative Expressiveness

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