On undecidability of propositional temporal logics on trace systems

Abstract

Partial order temporal logics are used frequently for specification and verification of concurrent systems [.5,6,14-17,19-211. These logics are more expressive than linear and branching time temporal logics. They allow for expressing partial order properties like serializability of database transactions [14,15], inevitability under concurrency fairness assumption [16], causal successor [19,20], layering of a program [6,15], snapshots or the concurrency of program segments [15,21]. The ability to require that certain actions be implemented concurrently is very important for system synthesis. For some of the attempts to synthesize programs from their specifications [1,11,18], we observe that in spite of the intention of synthesizing concurrent programs, the direct result of the given procedures is a sequential (often nondeterministic) program. To derive a concurrent program from this result, additional decomposition steps are called for. Peled and Pnueli write in [15]: “. . . The reason for this shortcoming that is inherent in these works is simply that the logics on which they are based