Safe BDD minimization using don't cares
DAC '97 Proceedings of the 34th annual Design Automation Conference
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
Efficient minimization of deterministic weak &ohgr;-automata
Information Processing Letters
Symbolic Model Checking
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Counting the solutions of Presburger equations without enumerating them
Theoretical Computer Science - Implementation and application automata
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
Action language verifier, extended
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Computing Convex Hulls by Automata Iteration
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Cost-Optimal Symbolic Planning with State Trajectory and Preference Constraints
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
A Generalization of Semenov's Theorem to Automata over Real Numbers
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
LIRA: handling constraints of linear arithmetics over the integers and the reals
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Mechanizing the powerset construction for restricted classes of ω-automata
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
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Automata are a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of bdds to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this paper, we generalize the notion of “don't cares” for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Büchi automaton (wdba) with respect to a given don't care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don't cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdbas.