Undecidability of Partial Order Logics

Abstract In this paper we prove the Undecidability of certain temporal logics over partial orders. Our proof is generic and can be applied to characterize various temporal operators that cannot be used for automatic verification (model checking).

[1]  Edmund M. Clarke,et al.  Characterizing Correctness Properties of Parallel Programs Using Fixpoints , 1980, ICALP.

[2]  Igor Walukiewicz,et al.  Difficult Configurations—On the Complexity of LTrL , 1998, Formal Methods Syst. Des..

[3]  Wojciech Penczek On Undecidability of Propositional Temporal Logics on Trace Systems , 1992, Inf. Process. Lett..

[4]  Rajeev Alur,et al.  Model-checking of correctness conditions for concurrent objects , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[5]  Pierre Wolper,et al.  A temporal logic for reasoning about partially ordered computations (Extended Abstract) , 1984, PODC '84.

[6]  Wieslaw Zielonka Safe Executions of Recognizable Trace Languages by Asynchronous Automata , 1989, Logic at Botik.

[7]  Rajeev Alur,et al.  Deciding Global Partial-Order Properties , 1998, Formal Methods Syst. Des..

[8]  Doron A. Peled,et al.  Interleaving set temporal logic , 1987, PODC '87.

[9]  Amir Pnueli,et al.  Proving Partial Order Properties , 1994, Theor. Comput. Sci..

[10]  Wojciech Penczek,et al.  Model-checking of causality properties , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

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

[12]  Wolfgang Reisig,et al.  Partial Order Semantics versus Interleaving Semantics for CSP-like Languages and its Impact on Fairness , 1984, ICALP.

[13]  Igor Walukiewicz,et al.  An expressively complete linear time temporal logic for Mazurkiewicz traces , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[14]  Antoni W. Mazurkiewicz,et al.  Trace Theory , 1986, Advances in Petri Nets.

[15]  Wieslaw Zielonka,et al.  Notes on Finite Asynchronous Automata , 1987, RAIRO Theor. Informatics Appl..