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Using Transitive–Closure Logic for Deciding Linear Properties of Monoids
[chapter]

2003
*
Lecture Notes in Computer Science
*

##
###
Page 2565 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

The author shows that (i)

*decidability**of*termination is not a modular*property**for*finite left-*linear*monadic TRSs, (ii)*decid*- ability*of*confluence and*decidability**of*completeness*of*(left- or right ... The rewrite relation*of*R and its reflexive and*transitive**closure*are denoted by = and =", respectively. ...##
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Page 7660 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

[Yu, Sheng] (3-WON-C; London, ON)
Transducers and the

*decidability**of*independence in free*monoids*. ... In partic- ular we demonstrate that the construction*of*the shape*of*a text can be formalized in terms*of*our monadic second-order*logic*. We briefly consider right-*linear*grammars*for*texts.” ...##
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Nondeterministic Phase Semantics and the Undecidability of Boolean BI

2013
*
ACM Transactions on Computational Logic
*

We deduce an embedding between trivial phase semantics

doi:10.1145/2422085.2422091
fatcat:4lz7blpptvhwvaebbqfdxwlb6i
*for*intuitionistic*linear**logic*(ILL) and Kripke semantics*for*BBI. ... We solve the open problem*of*the*decidability**of*Boolean BI*logic*(BBI), which can be considered as the core*of*Separation and Spatial*Logics*. ... Let → ⋆ M be the reflexive and*transitive**closure**of*the relation → M . ...##
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The Undecidability of Boolean BI through Phase Semantics

2010
*
2010 25th Annual IEEE Symposium on Logic in Computer Science
*

We solve the open problem

doi:10.1109/lics.2010.18
dblp:conf/lics/Larchey-WendlingG10
fatcat:mzc4on57jff7fd7deog4mzcc2e
*of*the*decidability**of*Boolean BI*logic*(BBI), which can be considered as the core*of*separation and spatial*logics*. ... We deduce an embedding between trivial phase semantics*for*intuitionistic*linear**logic*(ILL) and Kripke semantics*for*BBI. ... The authors dedicate this work and the resulting paper to the memory*of*Pr. Noëlle Carbonell. ...##
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Inverse Monoids: Decidability and Complexity of Algebraic Questions
[chapter]

2005
*
Lecture Notes in Computer Science
*

*For*the Cayley-graphs

*of*these

*monoids*, it is shown that the first-order theory with regular path predicates is

*decidable*. ... It is shown that

*for*every fixed

*monoid*

*of*this form the word problem can be solved both in

*linear*time on a RAM as well as in deterministic logarithmic space, which solves an open problem

*of*Margolis ... Acknowledgments We want to thank Arnaud Carayol, Didier Caucal, Volker Diekert, and Klaus-Jörn Lange

*for*fruitful discussion on the topic

*of*this paper. ...

##
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Inverse monoids: Decidability and complexity of algebraic questions

2007
*
Information and Computation
*

*For*the Cayley-graphs

*of*these

*monoids*, it is shown that the first-order theory with regular path predicates is

*decidable*. ... It is shown that

*for*every fixed

*monoid*

*of*this form the word problem can be solved both in

*linear*time on a RAM as well as in deterministic logarithmic space, which solves an open problem

*of*Margolis ... Acknowledgments We want to thank Arnaud Carayol, Didier Caucal, Volker Diekert, and Klaus-Jörn Lange

*for*fruitful discussion on the topic

*of*this paper. ...

##
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Page 3600 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

This is the reason

*for*introducing the new modalities ‘during’ and ‘pre- serves’, besides ‘ends’*used*in dynamic*logic*. V. R. ... Summary: “Dynamic*logic*is concerned with description and proof*of*‘before-after’ behaviour*of*programs. Process*logic*is an attempt to comprehend even*properties**of*on-going computations. ...##
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Algebraic recognizability of languages
[article]

2006
*
arXiv
*
pre-print

Recognizable languages

arXiv:cs/0609110v1
fatcat:2fnhr3gu5rdbbdugq76cqfvl4y
*of*finite words are part*of*every computer science cursus, and they are routinely described as a cornerstone*for*applications and*for*theory. ... We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed*for*modeling distributed or timed behaviors. ... Let*us*now assume that we are considering a*decidable*pseudovariety*of**monoids*(and hence a*decidable*variety*of*languages). ...##
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Page 5992 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
*
Mathematical Reviews
*

Paulo)

*Properties**of*recognizable 4 -subsets*of*a free*monoid*. ... We also study the*closure**properties**of*the above families under some operations.” {*For*the entire collection see MR 94f:68019.} ...##
###
Aperiodic String Transducers

2018
*
International Journal of Foundations of Computer Science
*

As corollaries, we obtain that FO definable string-to-string functions are equivalent to SST whose

doi:10.1142/s0129054118420054
fatcat:xi5qun7lgbgqddhieb3fgnwdcm
*transition**monoid*is finite and aperiodic, and to aperiodic copyless SST. ... We give the complexity*of*each construction and also prove that they preserve the aperiodicity*of*transducers. ... Let*us*also remark that the*transition**monoid**of*T does not depend on the output and is in fact the*transition**monoid**of*the underlying 2DFA. ...##
###
Page 9204 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

Summary: “In this work, we present some arithmetical and topo-

*logical**properties**of*Ising automata. ... In the paper one may find many interesting results concerning speeding up*linear*-time computations or*closure*prop- erties*of*some classes*of*languages. ...##
###
Algebraic Recognizability of Languages
[chapter]

2004
*
Lecture Notes in Computer Science
*

These equivalence results

doi:10.1007/978-3-540-28629-5_8
fatcat:5el7wd3umvgdzhw4dxukeugoci
*use*the specific structure*of*words (finite chains, labeled by the letters*of*the alphabet), and the*monoid*structure*of*the set*of*all words. ... In this paper, we concentrate on the algebraic notion*of*recognizability: that which,*for*finite words, exploits the*monoid*structure*of*the set*of*words, and relies on the consideration*of**monoid*morphisms ... Let*us*now assume that we are considering a*decidable*pseudovariety*of**monoids*(and hence a*decidable*variety*of*languages). ...##
###
Generalized rational relations and their logical definability
[chapter]

1997
*
Lecture Notes in Computer Science
*

In this paper we introduce the family

doi:10.1007/bfb0036178
fatcat:s5nzpjyncjeqfaz6io2crjvjoi
*of*generalized rational subsets*of*an arbitrary*monoid*as the*closure**of*the singletons under the Boolean operations, concatenation and Kleene star (just adding complementation ... The family*of*rational subsets*of*a direct product*of*free*monoids*Σ * 1 ×. . . ... Acknowledgment: one*of*the referees pointed out to*us*that Giovanni Pigghizzini proved in his PHD Thesis a similar result to our Lemma 4. ...##
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The semantics of BI and resource tableaux

2005
*
Mathematical Structures in Computer Science
*

As consequences

doi:10.1017/s0960129505004858
fatcat:n2gktzqns5d57pq3phcf6mlvcm
*of*the relationships between semantics*of*BI and resource tableaux, we prove two strong new results*for*propositional BI: its*decidability*and the finite model*property*with respect to ... The*logic**of*bunched implications, BI, provides a*logical*analysis*of*a basic notion*of*resource rich enough,*for*example, to form the*logical*basis*for*"pointer*logic*" and "separation*logic*" semantics ... We are grateful to Hongseok Yang, Peter O'Hearn, and the anonymous referees*for*their help with finding errors in, and with the presentation*of*, this long and complex paper. ...
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