Summary: A Really Temporal Logic \Lambday
Rajeev Alur Thomas A. Henzinger
AT&T Bell Laboratories Computer Science Department
600 Mountain Avenue Cornell University
Murray Hill, NJ 07974 Ithaca, NY 14853
Abstract. We introduce a temporal logic for the specification of realtime systems.
Our logic, TPTL, employs a novel quantifier construct for referencing time: the freeze
quantifier binds a variable to the time of the local temporal context. TPTL is both a
natural language for specification and a suitable formalism for verification. We present
a tableaubased decision procedure and a model checking algorithm for TPTL. Several
generalizations of TPTL are shown to be highly undecidable.
Linear temporal logic is a widely accepted language for specifying properties of reactive systems
and their behavior over time [Pnu77, OL82, MP92]. The tableaubased satisfiability algorithm
for its propositional version, PTL, forms the basis for the automatic verification and synthesis of
finitestate systems [LP84, MW84].
PTL is interpreted over models that abstract away from the actual times at which events
occur, retaining only temporal ordering information about the states of a system. The analysis
of systems with hard realtime requirements, such as bounded response time, calls, however, for
the development of formalisms with explicit time. Several attempts have been made to introduce