Succinct representations of graphs
Information and Control
Alternating automata, the weak monadic theory of the tree, and its complexity
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Statecharts: A visual formalism for complex systems
Science of Computer Programming
The complementation problem for Bu¨chi automata with applications to temporal logic
Theoretical Computer Science
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the power of bounded concurrency I: finite automata
Journal of the ACM (JACM)
Model checking and modular verification
ACM Transactions on Programming Languages and Systems (TOPLAS)
Reasoning about infinite computations
Information and Computation
Efficient generation of counterexamples and witnesses in symbolic model checking
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Journal of the ACM (JACM)
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
A Calculus of Communicating Systems
A Calculus of Communicating Systems
On the complexity of verifying concurrent transition systems
Information and Computation
Fast LTL to Büchi Automata Translation
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
CAV '90 Proceedings of the 2nd International Workshop on Computer Aided Verification
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
Alternating Refinement Relations
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Verification of Fair Transition Systems
Verification of Fair Transition Systems
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for natural proof systems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Shortest counterexamples for symbolic model checking of LTL with past
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Survey on Directed Model Checking
Model Checking and Artificial Intelligence
Lower Bounds on Witnesses for Nonemptiness of Universal Co-Büchi Automata
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Short witnesses and accepting lassos in ω-automata
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
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In the automata-theoretic approach to formal verification, the satisfiability and the model-checking problems for linear temporal logics are reduced to the nonemptiness problem of automata on infinite words. Modifying the nonemptiness algorithm to return a shortest witness to the nonemptiness (that is, a word of the form uvω that is accepted by the automaton and for which |uv| is minimal) has applications in synthesis and counterexample analysis. Unlike shortest accepting runs, which have been studied in the literature, the definition of shortest witnesses is semantic and is independent on the specification formalism of the property or the system. In particular, its robustness makes it appropriate for analyzing counterexamples of concurrent systems. We study the problem of finding shortest witnesses in automata with various types of concurrency. We show that while finding shortest witnesses is more complex than just checking nonemptiness in the nondeterministic and in the concurrent models of computation, it is not more complex in the alternating model. It follows that when the system is the composition of concurrent components, finding a shortest counterexample to its correctness is not harder than finding some counterexample. Our results give a computational motivation to translating temporal logic formulas to alternating automata, rather than going all the way to nondeterministic automata.