Expressiveness of propositional projection temporal logic with star

This paper investigates the expressiveness of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Buchi automata and @w-regular expressions are first extended as Stutter Buchi Automata (SBA) and Extended Regular Expressions (ERE) to include both finite and infinite strings. Further, by equivalent transformations among PPTL* formulas, SBAs and EREs, PPTL* is proved to represent exactly the full regular language. Moreover, some fragments of PPTL* are characterized, and finally, PPTL* and its fragments are classified into five different language classes.

[1]  Ben C. Moszkowski,et al.  Compositional reasoning about projected and infinite time , 1995, Proceedings of First IEEE International Conference on Engineering of Complex Computer Systems. ICECCS'95.

[2]  Maciej Koutny,et al.  Framed temporal logic programming , 2008, Sci. Comput. Program..

[3]  Zhenhua Duan,et al.  Alternating Interval Based Temporal Logics , 2010, ICFEM.

[4]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[5]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[6]  Moshe Y. Vardi.  A temporal fixpoint calculus , 1988, POPL '88.

[7]  Dean N. Arden.  Delayed-logic and finite-state machines , 1961, SWCT.

[8]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[9]  Benjamin Charles Moszkowski.  Reasoning about Digital Circuits , 1983 .

[10]  R. McNaughton,et al.  Counter-Free Automata , 1971 .

[11]  Li Zhang,et al.  A decision procedure for propositional projection temporal logic with infinite models , 2008, Acta Informatica.

[12]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[13]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[14]  Larry Joseph Stockmeyer,et al.  The complexity of decision problems in automata theory and logic , 1974 .

[15]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

[16]  Zhenhua Duan,et al.  An extended interval temporal logic and a framing technique for temporal logic programming , 1996 .

[17]  Jan van Leeuwen,et al.  Handbook Of Theoretical Computer Science, Vol. A , 1990 .

[18]  Amir Pnueli,et al.  Now you may compose temporal logic specifications , 1984, STOC '84.

[19]  Van Nguyen,et al.  Behavior: A Temporal Approach to Process Modelling , 1985, Logic of Programs.

[20]  Johan Anthory Willem Kamp,et al.  Tense logic and the theory of linear order , 1968 .

[21]  Gerard J. Holzmann,et al.  The Model Checker SPIN , 1997, IEEE Trans. Software Eng..

[22]  Zhenhua Duan,et al.  Model Checking Propositional Projection Temporal Logic Based on SPIN , 2007, ICFEM.

[23]  허윤정,et al.  Holzmann의 ˝The Model Checker SPIN˝에 대하여 , 1998 .

[24]  Saharon Shelah,et al.  On the temporal analysis of fairness , 1980, POPL '80.

[25]  Pierre Wolper.  Temporal Logic Can Be More Expressive , 1983, Inf. Control..

[26]  Amir Pnueli,et al.  A Choppy Logic , 1986, LICS.

[27]  Pierre Wolper,et al.  Yet Another Process Logic (Preliminary Version) , 1983, Logic of Programs.

[28]  Aravinda Prasad Sistla,et al.  Theoretical issues in the design and verification of distributed systems , 1983 .

[29]  Zhenhua Duan,et al.  Complexity of propositional projection temporal logic with star , 2009, Math. Struct. Comput. Sci..

[30]  Van Nguyen,et al.  A model and temporal proof system for networks of processes , 1985, POPL '85.

[31]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[32]  Philip Wadler,et al.  Experience with an applicative string processing language , 1980, POPL '80.