Efficient generation of counterexamples and witnesses in symbolic model checking
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Faster Algorithms for the Nonemptiness of Streett Automata and for Communication Protocol Pruning
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Approximation Hardness of TSP with Bounded Metrics
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
SIAM Journal on Computing
Complexity Theory: Exploring the Limits of Efficient Algorithms
Complexity Theory: Exploring the Limits of Efficient Algorithms
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Strategies for mainstream usage of formal verification
Proceedings of the 45th annual Design Automation Conference
25 Years of Model Checking: History, Achievements, Perspectives
25 Years of Model Checking: History, Achievements, Perspectives
Cheap and Small Counterexamples
SEFM '08 Proceedings of the 2008 Sixth IEEE International Conference on Software Engineering and Formal Methods
Formal methods: Practice and experience
ACM Computing Surveys (CSUR)
What went wrong: explaining counterexamples
SPIN'03 Proceedings of the 10th international conference on Model checking software
Minimal counterexample generation for SPIN
Proceedings of the 14th international SPIN conference on Model checking software
A note on on-the-fly verification algorithms
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Finding shortest witnesses to the nonemptiness of automata on infinite words
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Small strategies for safety games
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
RV'11 Proceedings of the Second international conference on Runtime verification
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Emptiness checking of ω-automata is a fundamental part of the automata-theoretic toolbox and is frequently applied in many applications, most notably verification of reactive systems. In this particular application, the capability to extract accepted words or alternatively accepting runs in case of non-emptiness is particularly useful, as these have a diagnostic value. However, non-optimised such words or runs can become huge, limiting their usability in practice, thus solutions with a small representation should be preferred. In this paper, we review the known results on obtaining these and complete the complexity landscape for all commonly used automaton types. We also prove upper and lower bounds on the approximation hardness of these problems.