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Pure Future Local Temporal Logics Are Expressively Complete for Mazurkiewicz Traces
[chapter]

2004
*
Lecture Notes in Computer Science
*

The paper settles a long standing problem

doi:10.1007/978-3-540-24698-5_27
fatcat:sesyyx3mfjbtvgxrw7yjscxan4
*for**Mazurkiewicz**traces*: the*pure**future**local**temporal**logic*defined with the basic modalities exists-next and until is*expressively**complete*. ... This means every first-order definable language of*Mazurkiewicz**traces*can be defined in a*pure**future**local**temporal**logic*. ... The following assertions*are*equivalent: We obtain also easily the same equivalence*for**trace*languages in R 1 . ...##
###
Pure future local temporal logics are expressively complete for Mazurkiewicz traces

2006
*
Information and Computation
*

The paper settles a long standing problem

doi:10.1016/j.ic.2006.07.002
fatcat:lebsg4ijfjcudg2gw2i5mlbqfa
*for**Mazurkiewicz**traces*: the*pure**future**local**temporal**logic*defined with the basic modalities exists-next and until is*expressively**complete*. ... This means every first-order definable language of*Mazurkiewicz**traces*can be defined in a*pure**future**local**temporal**logic*. ... The following assertions*are*equivalent: We obtain also easily the same equivalence*for**trace*languages in R 1 . ...##
###
From local to global temporal logics over Mazurkiewicz traces

2006
*
Theoretical Computer Science
*

Gastin,

doi:10.1016/j.tcs.2006.01.035
fatcat:djrx4v4opbeifdxr33xuzbjkca
*Pure**future**local**temporal**logics**are**expressively**complete**for**Mazurkiewicz**traces*, in: M. Farach-Colton (Ed.), Proc. LATIN'04, ... Gastin, LTL is*expressively**complete**for**Mazurkiewicz**traces*, J. Comput. System Sci. 64 (2002) 396-418] from the similar result on*local**temporal**logic*[V. Diekert, P. ... From this translation, using the*expressive**completeness*of*local**temporal**logics*with respect to first-order*logic*[11] we get as a corollary the*expressive**completeness*of global*temporal**logics*, which ...##
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Local LTL with Past Constants Is Expressively Complete for Mazurkiewicz Traces
[chapter]

2003
*
Lecture Notes in Computer Science
*

To obtain an

doi:10.1007/978-3-540-45138-9_37
fatcat:67e3kyxonnelboo6bxkil3dqya
*expressively**complete*linear-time*temporal**logic*(LTL) over*Mazurkiewicz**traces*that is computationally tractable, we need to intepret formulas*locally*, at individual events in a*trace*, rather ... In this paper, we show that it is possible to use unfiltered*future*modalities in conjunction with past constants and still obtain a*logic*that is*expressively**complete*over*traces*. ... Recently, in [10] , a*local**temporal**logic*has been defined over*traces*and shown to be*expressively**complete*and tractable (the satisfiability problem is in Pspace). ...##
###
Local Temporal Logic Is Expressively Complete for Cograph Dependence Alphabets
[chapter]

2001
*
Lecture Notes in Computer Science
*

Recently,

doi:10.1007/3-540-45653-8_4
fatcat:lpznamftszfdbizotea5kwm34y
*local**logics**for**Mazurkiewicz**traces**are*of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. ... If we focus on a*purely**local*interpretation of formulae at vertices (or events) of a*trace*, then the satisfiability problem of linear*temporal**logics*over*traces*turns out to be PSPACE-*complete*. ... In this paper, we*are*interested in the*expressive**completeness*of*pure**future**local**temporal**logics*. ...##
###
Local temporal logic is expressively complete for cograph dependence alphabets

2004
*
Information and Computation
*

Recently,

doi:10.1016/j.ic.2004.08.001
fatcat:w6dxltnqjjdifltipdwvdfdhn4
*local**logics**for**Mazurkiewicz**traces**are*of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. ... If we focus on a*purely**local*interpretation of formulae at vertices (or events) of a*trace*, then the satisfiability problem of linear*temporal**logics*over*traces*turns out to be PSPACE-*complete*. ... In this paper, we*are*interested in the*expressive**completeness*of*pure**future**local**temporal**logics*. ...##
###
LTL Is Expressively Complete for Mazurkiewicz Traces
[chapter]

2000
*
Lecture Notes in Computer Science
*

A long standing open problem in the theory of (

doi:10.1007/3-540-45022-x_18
fatcat:j3dr5b54vvbg3ljyxd2f3bpwve
*Mazurkiewicz*)*traces*has been the question whether LTL (linear*temporal**logic*) is*expressively**complete*with respect to the first order theory. ... We solve this problem positively*for*finite and infinite*traces*and*for*the simplest*temporal**logic*, which is based only on next and until modalities. ... The*expressive**completeness**for*a*pure**future**temporal**logic*LTL f was established in [2] . ...##
###
LTL Is Expressively Complete for Mazurkiewicz Traces

2002
*
Journal of computer and system sciences (Print)
*

A long standing open problem in the theory of (

doi:10.1006/jcss.2001.1817
fatcat:hnr3uxpqyzbvrfnvzzirz74eli
*Mazurkiewicz*)*traces*has been the question whether LTL (linear*temporal**logic*) is*expressively**complete*with respect to the first order theory. ... We solve this problem positively*for*finite and infinite*traces*and*for*the simplest*temporal**logic*, which is based only on next and until modalities. ... The*expressive**completeness**for*a*pure**future**temporal**logic*LTL f was established in [2] . ...##
###
A (non-elementary) modular decision procedure for LTrL
[chapter]

1998
*
Lecture Notes in Computer Science
*

Thiagarajan and Walukiewicz 18] have de ned a

doi:10.1007/bfb0055785
fatcat:d3kl2ufu6nccjka7yy7uwulp3a
*temporal**logic*LTrL on*Mazurkiewicz**traces*, patterned on the famous propositional*temporal**logic*of linear time LTL de ned by Pnueli. ... Since the*logic*LTrL is not*pure**future*, our algorithm constructs by induction a nite family of B uchi automata*for*each LTrL-formula. ... LTrL Thiagarajan and Walukiewicz 18] have proposed a*temporal**logic*on ( nite and in nite)*traces*, called LTrL, that is*expressively**complete*, i.e. equivalent to the rst-order*logic*FO(<) on ( nite and ...##
###
Temporal logics for concurrent recursive programs: Satisfiability and model checking

2014
*
Journal of Applied Logic
*

To specify properties of executions, we consider any

doi:10.1016/j.jal.2014.05.001
fatcat:2asz5h2ybvajxa6riyzmrnp5ze
*temporal**logic*whose modalities*are*definable in monadic second-order*logic*and that, in addition, allows PDL-like path*expressions*. ... This captures, in a unifying framework, a wide range of*logics*defined*for*ranked and unranked trees, nested words, and*Mazurkiewicz**traces*that have been studied separately. ... From Nested*Traces*to Trees Now, we transform a*temporal**logic*over nested*traces*into a*temporal**logic*over their tree encodings that "simulates" the original*logic*. ...##
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Temporal Logics for Concurrent Recursive Programs: Satisfiability and Model Checking
[chapter]

2011
*
Lecture Notes in Computer Science
*

To specify properties of executions, we consider any

doi:10.1007/978-3-642-22993-0_15
fatcat:taess7krsjbnznqf2rnnbdtkb4
*temporal**logic*whose modalities*are*definable in monadic second-order*logic*and that, in addition, allows PDL-like path*expressions*. ... This captures, in a unifying framework, a wide range of*logics*defined*for*ranked and unranked trees, nested words, and*Mazurkiewicz**traces*that have been studied separately. ... From Nested*Traces*to Trees Now, we transform a*temporal**logic*over nested*traces*into a*temporal**logic*over their tree encodings that "simulates" the original*logic*. ...##
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Wreath/Cascade Products and Related Decomposition Results for the Concurrent Setting of Mazurkiewicz Traces

2020
*
International Conference on Concurrency Theory
*

We develop a new algebraic framework to reason about languages of

doi:10.4230/lipics.concur.2020.19
dblp:conf/concur/AdsulGSW20
fatcat:yrkj2xutc5hspc7shkcpn7uijq
*Mazurkiewicz**traces*. ... The new framework is crucially used to propose a decomposition result*for*recognizable*trace*languages, which is an analogue of the Krohn-Rhodes theorem. ... arrive at a novel decomposition of aperiodic*trace*languages. ...##
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Interval logics and their decision procedures

1996
*
Theoretical Computer Science
*

We present an interval

doi:10.1016/0304-3975(95)00254-5
fatcat:kyfz6u6xejchzmp3vpfbakqd5q
*logic*, called*future*interval*logic*(FIL),*for*the specification and verification of concurrent systems. ...*temporal**logic*with "until" but no "next". ... We thank all four*for*their help. We*are*also very grateful to the anonymous referees*for*their careful reading, and*for*pointing out several errors in the first version. ...##
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Wreath/cascade products and related decomposition results for the concurrent setting of Mazurkiewicz traces (extended version)
[article]

2020
*
arXiv
*
pre-print

We develop a new algebraic framework to reason about languages of

arXiv:2007.07940v2
fatcat:mahusdkz7zcwrc2kvrowkkfxpa
*Mazurkiewicz**traces*. ... The new framework is crucially used to propose a decomposition result*for*recognizable*trace*languages, which is an analogue of the Krohn-Rhodes theorem. ... In paper [3] , a process based*pure**future**local**temporal**logic*is shown to be*expressively*equivalent to first order*logic*over*traces*. ...##
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A survey on the local divisor technique

2016
*
Theoretical Computer Science
*

These applications include linear

doi:10.1016/j.tcs.2015.07.008
fatcat:vsylzbqudrbobjlrsli3rghlpa
*temporal**logic*, rational*expressions*with Kleene stars restricted to prefix codes with bounded synchronization delay, Church-Rosser congruential languages, and Simon's ...*Local*divisors allow a powerful induction scheme on the size of a monoid. We survey this technique by giving several examples of this proof method. ... Acknowledgements We thank the anonymous reviewers*for*their numerous suggestions which significantly improved the presentation. ...
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