Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Counterexample-guided predicate abstraction of hybrid systems
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
A Policy Iteration Technique for Time Elapse over Template Polyhedra
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Precise Interval Analysis vs. Parity Games
FM '08 Proceedings of the 15th international symposium on Formal Methods
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
Computing relaxed abstract semantics w.r.t. quadratic zones precisely
SAS'10 Proceedings of the 17th international conference on Static analysis
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Improving strategies via SMT solving
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Precise relational invariants through strategy iteration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Computing over-approximations of all possible time trajectories is an important task in the analysis of hybrid systems. Sankaranarayanan et al. [20] suggested to approximate the set of reachable states using template polyhedra. In the present paper, we use a max-strategy improvement algorithm for computing an abstract semantics for affine hybrid automata that is based on template polyhedra and safely over-approximates the concrete semantics. Based on our formulation, we show that the corresponding abstract reachability problem is in co-NP. Moreover, we obtain a polynomial-time algorithm for the time elapse operation over template polyhedra.