TY - GEN

T1 - Co-ing büchi made tight and useful

AU - Boker, Udi

AU - Kupferman, Orna

PY - 2009

Y1 - 2009

N2 - We solve the longstanding open problems of the blowup involved in the translations (when possible) of a nondeterministic Büchi word automaton (NBW) to a nondeterministic co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW). For the NBW to NCW translation, the currently known upper bound is 2O(n log n) and the lower bound is 1:5n. We improve the upper bound to n2n and describe a matching lower bound of 2(n). For the NBW to DCW translation, the currently known upper bound is 2O(n log n). We improve it to 2O(n which is asymptotically tight. Both of our upper-bound constructions are based on a simple subset construction, do not involve intermediate automata with richer acceptance conditions and can be implemented symbolically. We point to numerous applications of the new constructions. In particular they imply a simple subset-construction based translation (when possible) of LTL to deterministic Büchi word automata.

AB - We solve the longstanding open problems of the blowup involved in the translations (when possible) of a nondeterministic Büchi word automaton (NBW) to a nondeterministic co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW). For the NBW to NCW translation, the currently known upper bound is 2O(n log n) and the lower bound is 1:5n. We improve the upper bound to n2n and describe a matching lower bound of 2(n). For the NBW to DCW translation, the currently known upper bound is 2O(n log n). We improve it to 2O(n which is asymptotically tight. Both of our upper-bound constructions are based on a simple subset construction, do not involve intermediate automata with richer acceptance conditions and can be implemented symbolically. We point to numerous applications of the new constructions. In particular they imply a simple subset-construction based translation (when possible) of LTL to deterministic Büchi word automata.

UR - http://www.scopus.com/inward/record.url?scp=70350592169&partnerID=8YFLogxK

U2 - 10.1109/LICS.2009.32

DO - 10.1109/LICS.2009.32

M3 - Conference contribution

AN - SCOPUS:70350592169

SN - 9780769537467

T3 - Proceedings - Symposium on Logic in Computer Science

SP - 245

EP - 254

BT - Proceedings - 2009 24th Annual IEEE Symposium on Logic In Computer Science, LICS 2009

T2 - 2009 24th Annual IEEE Symposium on Logic In Computer Science, LICS 2009

Y2 - 11 August 2009 through 14 August 2009

ER -