A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Decidability, Complexity, and Expressiveness of First-Order Logic Over the Subword Ordering
[article]

2021
*
arXiv
*
pre-print

We consider

arXiv:1701.07470v2
fatcat:zkrsawlwfvdqnkbepnaz2wjxxm
*first*-*order**logic**over**the**subword**ordering*on finite words, where each word is available as a constant. Our*first*result is that*the*Σ_1 theory is undecidable (already*over*two letters). ... entire*first*-*order*theory is*decidable*. ...*The**logic**of**subwords*. In this paper we consider*the**first*-*order**logic*FO(A * , ⊑)*of*words*over*some alphabet A = {a, b, c, . . .} equipped with*the**subword*relation ⊑. ...##
###
Complexity of Counting First-Order Logic for the Subword Order

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

for

doi:10.4230/lipics.mfcs.2020.61
dblp:conf/mfcs/KuskeS20
fatcat:ydanpbabhfgyzayqcvbdd5scpa
*first*-*order**logic*). ... This paper considers*the*structure consisting*of**the*set*of*all words*over*a given alphabet together with*the**subword*relation, regular predicates,*and*constants for every word. ... M F C S 2 0 2 0 61:10*Complexity**of*Counting*First*-*Order**Logic*for*the**Subword**Order*For*first*-*order*formulas ϕ, this result can be found in [7, Cor. 7.4*and*Thm. 7.5] . ...##
###
Graph Logics with Rational Relations and the Generalized Intersection Problem

2012
*
2012 27th Annual IEEE Symposium on Logic in Computer Science
*

Such

doi:10.1109/lics.2012.23
dblp:conf/lics/BarceloFL12
fatcat:wnixhv57lfat5f5ccz3ll7ir74
*logics*use conditions on paths*expressed*by regular languages*and*relations, but they often need to be extended by rational relations such as*subword*(factor) or subsequence. ... We prove that for several basic*and*commonly used rational relations,*the*intersection problem with regular relations is either undecidable (e.g., for*subword*or suffix,*and*some generalizations), or*decidable*...*The*NLOGSPACE-data*complexity*matches that*of*RPQs, CRPQs,*and*ECRPQs [15] , [16] , [3] ,*and**the*combined*complexity*matches that*of**first*-*order**logic*, or ECRPQs without extra relations. ...##
###
Page 1068 of Mathematical Reviews Vol. , Issue 91B
[page]

1991
*
Mathematical Reviews
*

This approach allows us to construct

*first*-*order*theories in which lambda-abstraction*and*quantification can be easily*expressed*as terms*of**the*language.” ...*The*present paper contains new results in*the*case*of*infinite words with linear*subword**complexity*,*and*Sturmian words as a particular case. ...##
###
Languages Ordered by the Subword Order
[chapter]

2019
*
Green Chemistry and Sustainable Technology
*

For such structures, we consider

doi:10.1007/978-3-030-17127-8_20
dblp:conf/fossacs/KuskeZ19
fatcat:umgwvovfnzftrdsn7375axk6wa
*the*extension*of**first*-*order**logic*by threshold-*and*modulo-counting quantifiers. ... These results extend earlier ones where only*the*language*of*all words without*the*cover relation*and*fragments*of**first*-*order**logic*were considered. ... We are interested in*logics**over**the**subword**order*. Prior work on this has concentrated on*first*-*order**logic*where*the*universe consists*of*all words*over*some alphabet. ...##
###
Graph Logics with Rational Relations

2013
*
Logical Methods in Computer Science
*

Such

doi:10.2168/lmcs-9(3:1)2013
fatcat:lk6o6mmsyfhtxm5xpp7zusnmbm
*logics*use conditions on paths*expressed*by regular languages*and*relations, but they often need to be extended by rational relations such as*subword*or subsequence. ... We prove that for several basic*and*commonly used rational relations,*the*intersection problem with regular relations is either undecidable (e.g., for*subword*or suffix,*and*some generalizations), or*decidable*...*of**logical*queries*over*graphs. ...##
###
Graph logics with rational relations

2014
*
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14
*

Such

doi:10.1145/2603088.2603122
dblp:conf/csl/BarceloM14
fatcat:gp3braivgnbd5cucl5n5rhku24
*logics*use conditions on paths*expressed*by regular languages*and*relations, but they often need to be extended by rational relations such as*subword*or subsequence. ... We prove that for several basic*and*commonly used rational relations,*the*intersection problem with regular relations is either undecidable (e.g., for*subword*or suffix,*and*some generalizations), or*decidable*...*of**logical*queries*over*graphs. ...##
###
Languages ordered by the subword order
[article]

2019
*
arXiv
*
pre-print

For such structures, we consider

arXiv:1901.02194v1
fatcat:akjmbq7rgzdplpi2fmyl54dq6m
*the*extension*of**first*-*order**logic*by threshold-*and*modulo-counting quantifiers. ... These results extend earlier ones where only*the*language*of*all words without*the*cover relation*and*fragments*of**first*-*order**logic*were considered. ... Thus, to get a*decidable*theory, one has to restrict*the**expressiveness**of**first*-*order**logic*considerably. ...##
###
Graph Logics with Rational Relations

2017
*
ACM Transactions on Computational Logic
*

Such

doi:10.1145/3070822
fatcat:caif435stjaxxkzihykoetrvmy
*logics*use conditions on paths*expressed*by regular languages*and*relations, but they often need to be extended by rational relations such as*subword*or subsequence. ... We prove that for several basic*and*commonly used rational relations,*the*intersection problem with regular relations is either undecidable (e.g., for*subword*or suffix,*and*some generalizations), or*decidable*...*of**logical*queries*over*graphs. ...##
###
The complexity of first-order and monadic second-order logic revisited

2004
*
Annals of Pure and Applied Logic
*

We establish a number

doi:10.1016/j.apal.2004.01.007
fatcat:ujya375lw5a7vdx7njjjgur5qy
*of*similar lower bounds for*the*model-checking problem for*first*-*order**logic*, for example, on*the*class*of*all trees. ... In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for*first*-*order**and*monadic second-*order**logic*. ... A well-known result*of*Kamp [12] states that LTL*and**first*-*order**logic*have*the*same*expressive*power on words. ...##
###
Two-variable logic on data words

2011
*
ACM Transactions on Computational Logic
*

It should be noted however that full monadic second-

doi:10.1145/1970398.1970403
fatcat:5hpqzonhwnaatkdbg2fr5tdfpq
*order**logic*(*and*even*first*-*order**logic*)*over*data words is known to be undecidable [NSV04] . ... In this sense,*the**decidability**of*EMSO 2 (∼, <, +1) can be seen as an extension*of**the*classical*decidability*result*of*monadic second-*order**logic**over*words. ...*Over*graphs or*over*arbitrary relational structures,*first*-*order**logic*is undecidable, while its two-variable fragment is*decidable*[Mor75] . ...##
###
CaRet With Forgettable Past

2009
*
Electronical Notes in Theoretical Computer Science
*

*The*

*logic*CaRet is less

*expressive*than NVPA

*and*is easily

*expressible*in

*the*

*first*-

*order*fragment FO μ

*of*MSO μ . However, it is an open question whether CaRet is FO μ -complete [1]. ... This situation is quite different from

*the*

*logic*PLTL, for which

*the*separation property ensures that LTL has

*the*same

*expressiveness*as PLTL

*and*, thus, corresponds to

*the*class

*of*sentences

*of*

*the*

*first*-

*order*... Then, in Subsection 3.2, we show that NCaRet is

*expressively*complete for

*the*

*first*

*order*fragment FO μ

*of*MSO μ [3] , which extends

*the*classical monadic second

*order*

*logic*(MSO)

*over*words with a binary ...

##
###
Separability by Short Subsequences and Subwords

2015
*
International Conference on Database Theory
*

We study

doi:10.4230/lipics.icdt.2015.230
dblp:conf/icdt/HofmanM15
fatcat:kkzjyetwyvhxldcc57nb4o24gu
*the**complexity**of*separability*of*regular languages by combinations*of*subsequences or*subwords**of*a given length k. ... Typically, S comes from a simple, less*expressive*class*of*languages than I*and*E. ... We would like to thank*the*anonymous reviewers*of*ICDT 2015 for many helpful remarks. This work was supported by DFG grant MA4938/2-1. ...##
###
The height of piecewise-testable languages and the complexity of the logic of subwords
[article]

2019
*
arXiv
*
pre-print

As an application

arXiv:1511.01807v4
fatcat:txe7kv7yejchvf3yb2e3ngxysu
*of*these results, we show that FO^2(A^*,),*the*two-variable fragment*of**the**first*-*order**logic**of*sequences with*the**subword**ordering*, can only*express*piecewise-testable properties*and*...*The*height*of*a piecewise-testable language L is*the*maximum length*of**the*words needed to define L by excluding*and*requiring given*subwords*. ... Acknowledgments We thank*the*anonymous reviewers for their many helpful suggestions. ...##
###
The height of piecewise-testable languages and the complexity of the logic of subwords

2019
*
Logical Methods in Computer Science
*

As an application

doi:10.23638/lmcs-15(2:6)2019
fatcat:jvnwivjvx5atldjbijcqnvc3sy
*of*these results, we show that $\mathsf{FO}^2(A^*,\sqsubseteq)$,*the*two-variable fragment*of**the**first*-*order**logic**of*sequences with*the**subword**ordering*, can only*express*piecewise-testable ...*The*height*of*a piecewise-testable language $L$ is*the*maximum length*of**the*words needed to define $L$ by excluding*and*requiring given*subwords*. ... Acknowledgments We thank*the*anonymous reviewers for their many helpful suggestions. ...
« Previous

*Showing results 1 — 15 out of 1,169 results*