On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of theoretical computer science (vol. B)
Reasoning about infinite computations
Information and Computation
Computer-aided verification of coordinating processes: the automata-theoretic approach
Computer-aided verification of coordinating processes: the automata-theoretic approach
Journal of the ACM (JACM)
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Safraless compositional synthesis
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Finding shortest witnesses to the nonemptiness of automata on infinite words
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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The nonemptiness problem for nondeterministic automata on infinite words can be reduced to a sequence of reachability queries. The length of a shortest witness to the nonemptiness is then polynomial in the automaton. Nonemptiness algorithms for alternating automata translate them to nondeterministic automata. The exponential blow-up that the translation involves is justified by lower bounds for the nonemptiness problem, which is exponentially harder for alternating automata. The translation to nondeterministic automata also entails a blow-up in the length of the shortest witness. A matching lower bound here is known for cases where the translation involves a 2 O (n ) blow up, as is the case for finite words or Büchi automata. Alternating co-Büchi automata and witnesses to their nonemptiness have applications in model checking (complementing a nondeterministic Büchi word automaton results in a universal co-Büchi automaton) and synthesis (an LTL specification can be translated to a universal co-Büchi tree automaton accepting exactly all the transducers that realize it). Emptiness algorithms for alternating co-Büchi automata proceed by a translation to nondeterministic Büchi automata. The blow up here is 2 O (n logn ), and it follows from the fact that, on top of the subset construction, the nondeterministic automaton maintains ranks to the states of the alternating automaton. It has been conjectured that this super-exponential blow-up need not apply to the length of the shortest witness. Intuitively, since co-Büchi automata are memoryless, it looks like a shortest witness need not visit a state associated with the same set of states more than once. A similar conjecture has been made for the width of a transducer generating a tree accepted by an alternating co-Büchi tree automaton. We show that, unfortunately, this is not the case, and that the super-exponential lower bound on the witness applies already for universal co-Büchi word and tree automata.