A real-time interval logic and its decision procedure

Real-Time Future Interval Logic is a visual logic in which formulae have a natural graphical representation, resembling timing diagrams. It is a dense real-time temporal logic that is based on two simple temporal primitives: interval modalities for the purely qualitative part and duration predicates for the quantitative part. We give a decision procedure for the logic by reduction to the emptiness problem for Timed Buchi Automata. The decision procedure forms the core of a proof checker for the logic that we have recently implemented. The logic does not admit instantaneous states, and is invariant under realtime stuttering. These properties facilitate proof methods based on abstraction and refinement. Two natural extensions of the logic lead to nonelementariness and undecidability.

[1]  Rajeev Alur,et al.  Timing Verification by Successive Approximation , 1992, Inf. Comput..

[2]  Zohar Manna,et al.  From Timed to Hybrid Systems , 1991, REX Workshop.

[3]  Thomas A. Henzinger,et al.  Symbolic Model Checking for Real-Time Systems , 1994, Inf. Comput..

[4]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[5]  P. M. Melliar-Smith.  Extending Interval Logic to Real Time Systems , 1987, Temporal Logic in Specification.

[6]  Louise E. Moser,et al.  An Automata-Theoretic Decision Procedure for Future Interval Logic , 1992, FSTTCS.

[7]  Michael R. Hansen,et al.  Decidability and Undecidability Results for Duration Calculus , 1993, STACS.

[8]  Louise E. Moser,et al.  Graphical specifications for concurrent software systems , 1992, International Conference on Software Engineering.

[9]  P. M. Melliar-Smith,et al.  An interval logic for higher-level temporal reasoning , 1983, PODC '83.

[10]  Louise E. Moser,et al.  Really visual temporal reasoning , 1993, 1993 Proceedings Real-Time Systems Symposium.

[11]  M. Newman.  On Theories with a Combinatorial Definition of "Equivalence" , 1942 .

[12]  Leslie Lamport,et al.  The temporal logic of actions , 1994, TOPL.

[13]  David L. Dill,et al.  Timing Assumptions and Verification of Finite-State Concurrent Systems , 1989, Automatic Verification Methods for Finite State Systems.

[14]  A. Prasad Sistla,et al.  Quantitative Temporal Reasoning , 1990, CAV.

[15]  Zohar Manna,et al.  A Hardware Semantics Based on Temporal Intervals , 1983, ICALP.

[16]  Thomas A. Henzinger,et al.  The benefits of relaxing punctuality , 1991, JACM.

[17]  Louise E. Moser,et al.  A Graphical Interval Logic Toolset for Verifying Concurrent Systems , 1993, CAV.

[18]  Michael M. Gorlick,et al.  Real-time interval logic for reasoning about executions of real-time programs , 1989 .

[19]  Thomas A. Henzinger,et al.  A really temporal logic , 1994, JACM.

[20]  Amir Pnueli,et al.  A really abstract concurrent model and its temporal logic , 1986, POPL '86.

[21]  Harry R. Lewis,et al.  A logic of concrete time intervals , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[22]  Pierre Wolper,et al.  On the Relation of Programs and Computations to Models of Temporal Logic , 1987, Temporal Logic in Specification.

[23]  Thomas A. Henzinger,et al.  Parametric real-time reasoning , 1993, STOC.

[24]  Thomas A. Henzinger,et al.  Back to the future: towards a theory of timed regular languages , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[25]  A. A. Aaby,et al.  Specification of real-time systems in real-time temporal interval logic , 1988, Proceedings. Real-Time Systems Symposium.

[26]  R. Smullyan.  First-Order Logic , 1968 .

[27]  Aloysius K. Mok,et al.  Safety analysis of timing properties in real-time systems , 1986, IEEE Transactions on Software Engineering.

[28]  Louise E. Moser,et al.  A graphical interval logic for specifying concurrent systems , 1994, TSEM.

[29]  C. A. R. Hoare,et al.  A Calculus of Durations , 1991, Inf. Process. Lett..