What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Making abstract interpretations complete
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Automata, Languages, and Machines
Automata, Languages, and Machines
Refining Model Checking by Abstract Interpretation
Automated Software Engineering
Model Checking of Real-Time Reachability Properties Using Abstractions
TACAS '98 Proceedings of the 4th International Conference on Tools and Algorithms for Construction and Analysis of Systems
TACAS '99 Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems
TACAs '96 Proceedings of the Second International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Accurate Widenings and Boundedness Properties of Timed Systems
PSI '02 Revised Papers from the 4th International Andrei Ershov Memorial Conference on Perspectives of System Informatics: Akademgorodok, Novosibirsk, Russia
Beyond Region Graphs: Symbolic Forward Analysis of Timed Automata
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
A New Class of Decidable Hybrid Systems
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Optimality in Abstractions of Model Checking
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Generating Finite-State Abstractions of Reactive Systems Using Decision Procedures
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Experience with Predicate Abstraction
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Abstract and Model Check While You Prove
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Symbolic Techniques for Parametric Reasoning about Counter and Clock Systems
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Counterexample-Guided Abstraction Refinement
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Syntactic Program Transformations for Automatic Abstraction
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Verifying Liveness by Augmented Abstraction
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Model Checking Guided Abstraction and Analysis
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
HYTECH: A Model Checker for Hybrid Systems
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Multiple Counters Automata, Safety Analysis and Presburger Arithmetic
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
General decidability theorems for infinite-state systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Compositional and symbolic model-checking of real-time systems
RTSS '95 Proceedings of the 16th IEEE Real-Time Systems Symposium
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Symbolic forward analysis is a semi-algorithm that in many cases solves the model checking problem for infinite state systems in practice. This semi-algorithm is implemented in manypractical model checking tools like UPPAAL [BLL+96], KRONOS [DT98] and HYTECH [HHWT97]. In most practical experiments, termination of symbolic forward analysis is achieved by employing abstractions resulting in an abstract symbolic forward analysis. This paper presents a unified algebraic framework for deriving and reasoning about abstract symbolic forward analysis procedures for a large class of infinite state systems with variables ranging over a numeric domain. The framework is obtained by lifting notions from classical algebraic theoryof automata to constraints representing sets of states. Our framework provides sufficient conditions under which the derived abstract symbolic forward analysis procedure is always terminating or accurate or both. The class of infinite state systems that we consider here are (possibly non-linear) hybrid systems and (possiblynon-linear) integer-valued systems. The central notions involved are those of constraint transformer monoids and coverings between constraint transformer monoids. We show concrete applications of our framework in deriving abstract symbolic forward analysis algorithms for timed automata and the two process bakeryalgorithm that are both terminating and accurate.