Descriptive Complexity, Lower Bounds and Linear Time

Schwentick, Thomas

doi:10.1007/10703163_2

Cited by 4 publications

(3 citation statements)

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“…Descriptive complexity measures the syntactic complexity of formulae that express a certain property, instead of its computation complexity. See [5] and [9] for more general discussions on this theory. A fundamental result in this area is the well-known Fagin's theorem, which states that a property is in the class NP (non-deterministic polynomial time computability) if and only if it is describable as an existential second-order logical sentence (see [3]).…”

Section: Introductionmentioning

confidence: 99%

Existential monadic second order logic on random rooted trees

Holroyd

Levy

Podder

et al. 2019

Discrete Mathematics

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Section: Introductionmentioning

confidence: 99%

Existential monadic second order logic on random rooted trees

Holroyd

Levy

Podder

et al. 2019

Discrete Mathematics

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“…. , t n of strings, decide whether 2 is the lexicographically sorted version of 1 ) which are conjectured not to belong to DTIME(n) (see [24]). In the present paper we show the following analogue of the result of [11]: One area of research in Finite Model Theory considers extensions of logics which allow invariant uses of some auxiliary relations.…”

Section: Introductionmentioning

confidence: 99%

On the Expressive Power of Monadic Least Fixed Point Logic

Schweikardt

2004

Automata, Languages and Programming

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Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of first-order logic FO and monadic second-order logic MSO. In this paper we take a closer look at the expressive power of MLFP. Our results are 1. MLFP can describe graph properties beyond any fixed level of the monadic second-order quantifier alternation hierarchy. 2. On strings with built-in addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN. 3. Settling the question whether addition-invariant MLFP ? = addition-invariant MSO on finite strings would solve open problems in complexity theory: "=" would imply that PH = PTIME whereas " =" would imply that DLIN = LINH.

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“…. , t n of strings, decide whether 2 is the lexicographically sorted version of 1 ) which are conjectured not to belong to DTIME(n) (see [28]). In the present paper we show the following analogue of the result of [13]: Theorem 1.2.…”

mentioning

confidence: 99%

On the expressive power of monadic least fixed point logic

Schweikardt

2006

Theoretical Computer Science

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Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of first-order logic FO and monadic second-order logic MSO. In this paper, we take a closer look at the expressive power of MLFP. Our results are:(1) MLFP can describe graph properties beyond any fixed level of the monadic second-order quantifier alternation hierarchy.(2) On strings with built-in addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN. (3) Settling the question whether addition-invariant MLFP ? = addition-invariant MSO on finite strings or, equivalently, settling the question whether MLFP ? = MSO on finite strings with additionwould solve open problems in complexity theory: "=" would imply that PH = PTIME whereas " =" would imply that DLIN = LINH.Apart from this we give a self-contained proof of the previously known result that MLFP is strictly less expressive than MSO on the class of finite graphs.

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Descriptive Complexity, Lower Bounds and Linear Time

Cited by 4 publications

References 43 publications

Existential monadic second order logic on random rooted trees

Existential monadic second order logic on random rooted trees

On the Expressive Power of Monadic Least Fixed Point Logic

On the expressive power of monadic least fixed point logic

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