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

Christian Delhommé, Teodor Knapik, D. Gnanaraj Thomas
2003 Lecture Notes in Computer Science  
doi:10.1007/978-3-540-45138-9_32 fatcat:7qucbqbglbestck6neaz36vsci

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.  ... 

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.”  ... 

Nondeterministic Phase Semantics and the Undecidability of Boolean BI

Dominique Larchey-Wendling, Didier Galmiche
2013 ACM Transactions on Computational Logic  
We deduce an embedding between trivial phase semantics 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 .  ... 
doi:10.1145/2422085.2422091 fatcat:4lz7blpptvhwvaebbqfdxwlb6i

The Undecidability of Boolean BI through Phase Semantics

Dominique Larchey-Wendling, Didier Galmiche
2010 2010 25th Annual IEEE Symposium on Logic in Computer Science  
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.  ...  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.  ... 
doi:10.1109/lics.2010.18 dblp:conf/lics/Larchey-WendlingG10 fatcat:mzc4on57jff7fd7deog4mzcc2e

Inverse Monoids: Decidability and Complexity of Algebraic Questions [chapter]

Markus Lohrey, Nicole Ondrusch
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.  ... 
doi:10.1007/11549345_57 fatcat:fkjpxsguojbfxkv57fos4lcgqm

Inverse monoids: Decidability and complexity of algebraic questions

Markus Lohrey, Nicole Ondrusch
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.  ... 
doi:10.1016/j.ic.2007.01.002 fatcat:b53ikr7syfgkbith47hrc3c4ge

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.  ... 

Algebraic recognizability of languages [article]

Pascal Weil
2006 arXiv   pre-print
Recognizable languages 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).  ... 
arXiv:cs/0609110v1 fatcat:2fnhr3gu5rdbbdugq76cqfvl4y

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

Luc Dartois, Ismaël Jecker, Pierre-Alain Reynier
2018 International Journal of Foundations of Computer Science  
As corollaries, we obtain that FO definable string-to-string functions are equivalent to SST whose 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.  ... 
doi:10.1142/s0129054118420054 fatcat:xi5qun7lgbgqddhieb3fgnwdcm

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]

Pascal Weil
2004 Lecture Notes in Computer Science  
These equivalence results 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).  ... 
doi:10.1007/978-3-540-28629-5_8 fatcat:5el7wd3umvgdzhw4dxukeugoci

Generalized rational relations and their logical definability [chapter]

Christian Choffrut, Leucio Guerra
1997 Lecture Notes in Computer Science  
In this paper we introduce the family 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.  ... 
doi:10.1007/bfb0036178 fatcat:s5nzpjyncjeqfaz6io2crjvjoi

The semantics of BI and resource tableaux

D. GALMICHE, D. MÉRY, D. PYM
2005 Mathematical Structures in Computer Science  
As consequences 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.  ... 
doi:10.1017/s0960129505004858 fatcat:n2gktzqns5d57pq3phcf6mlvcm
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