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

Volker Diekert, Paul Gastin
2004 Lecture Notes in Computer Science  
The paper settles a long standing problem 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 .  ... 
doi:10.1007/978-3-540-24698-5_27 fatcat:sesyyx3mfjbtvgxrw7yjscxan4

Pure future local temporal logics are expressively complete for Mazurkiewicz traces

Volker Diekert, Paul Gastin
2006 Information and Computation  
The paper settles a long standing problem 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 .  ... 
doi:10.1016/j.ic.2006.07.002 fatcat:lebsg4ijfjcudg2gw2i5mlbqfa

From local to global temporal logics over Mazurkiewicz traces

Volker Diekert, Paul Gastin
2006 Theoretical Computer Science  
Gastin, 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  ... 
doi:10.1016/j.tcs.2006.01.035 fatcat:djrx4v4opbeifdxr33xuzbjkca

Local LTL with Past Constants Is Expressively Complete for Mazurkiewicz Traces [chapter]

Paul Gastin, Madhavan Mukund, K. Narayan Kumar
2003 Lecture Notes in Computer Science  
To obtain an 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).  ... 
doi:10.1007/978-3-540-45138-9_37 fatcat:67e3kyxonnelboo6bxkil3dqya

Local Temporal Logic Is Expressively Complete for Cograph Dependence Alphabets [chapter]

Volker Diekert, Paul Gastin
2001 Lecture Notes in Computer Science  
Recently, 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.  ... 
doi:10.1007/3-540-45653-8_4 fatcat:lpznamftszfdbizotea5kwm34y

Local temporal logic is expressively complete for cograph dependence alphabets

Volker Diekert, Paul Gastin
2004 Information and Computation  
Recently, 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.  ... 
doi:10.1016/j.ic.2004.08.001 fatcat:w6dxltnqjjdifltipdwvdfdhn4

LTL Is Expressively Complete for Mazurkiewicz Traces [chapter]

Volker Diekert, Paul Gastin
2000 Lecture Notes in Computer Science  
A long standing open problem in the theory of (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] .  ... 
doi:10.1007/3-540-45022-x_18 fatcat:j3dr5b54vvbg3ljyxd2f3bpwve

LTL Is Expressively Complete for Mazurkiewicz Traces

Volker Diekert, Paul Gastin
2002 Journal of computer and system sciences (Print)  
A long standing open problem in the theory of (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] .  ... 
doi:10.1006/jcss.2001.1817 fatcat:hnr3uxpqyzbvrfnvzzirz74eli

A (non-elementary) modular decision procedure for LTrL [chapter]

Paul Gastin, Raphaël Meyer, Antoine Petit
1998 Lecture Notes in Computer Science  
Thiagarajan and Walukiewicz 18] have de ned a 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  ... 
doi:10.1007/bfb0055785 fatcat:d3kl2ufu6nccjka7yy7uwulp3a

Temporal logics for concurrent recursive programs: Satisfiability and model checking

Benedikt Bollig, Aiswarya Cyriac, Paul Gastin, Marc Zeitoun
2014 Journal of Applied Logic  
To specify properties of executions, we consider any 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.  ... 
doi:10.1016/j.jal.2014.05.001 fatcat:2asz5h2ybvajxa6riyzmrnp5ze

Temporal Logics for Concurrent Recursive Programs: Satisfiability and Model Checking [chapter]

Benedikt Bollig, Aiswarya Cyriac, Paul Gastin, Marc Zeitoun
2011 Lecture Notes in Computer Science  
To specify properties of executions, we consider any 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.  ... 
doi:10.1007/978-3-642-22993-0_15 fatcat:taess7krsjbnznqf2rnnbdtkb4

Wreath/Cascade Products and Related Decomposition Results for the Concurrent Setting of Mazurkiewicz Traces

Bharat Adsul, Paul Gastin, Saptarshi Sarkar, Pascal Weil, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
We develop a new algebraic framework to reason about languages of 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.  ... 
doi:10.4230/lipics.concur.2020.19 dblp:conf/concur/AdsulGSW20 fatcat:yrkj2xutc5hspc7shkcpn7uijq

Interval logics and their decision procedures

Y.S Ramakrishna, P.M Melliar-Smith, L.E Moser, L.K Dillon, G Kutty
1996 Theoretical Computer Science  
We present an interval 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.  ... 
doi:10.1016/0304-3975(95)00254-5 fatcat:kyfz6u6xejchzmp3vpfbakqd5q

Wreath/cascade products and related decomposition results for the concurrent setting of Mazurkiewicz traces (extended version) [article]

Bharat Adsul, Paul Gastin, Saptarshi Sarkar, Pascal Weil
2020 arXiv   pre-print
We develop a new algebraic framework to reason about languages of 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.  ... 
arXiv:2007.07940v2 fatcat:mahusdkz7zcwrc2kvrowkkfxpa

A survey on the local divisor technique

Volker Diekert, Manfred Kufleitner
2016 Theoretical Computer Science  
These applications include linear 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.  ... 
doi:10.1016/j.tcs.2015.07.008 fatcat:vsylzbqudrbobjlrsli3rghlpa
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