A hierarchy of temporal properties (invited paper, 1989)
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Reasoning about infinite computations
Information and Computation
An Until hierarchy and other applications of an Ehrenfeucht-Fraïssé game for temporal logic
Information and Computation - Special issue: LICS 1996—Part 1
Characterization of Temporal Property Classes
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Alternating Automata and Logics over Infinite Words
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Fast LTL to Büchi Automata Translation
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Alternating Automata: Unifying Truth and Validity Checking for Temporal Logics
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Temporal logic and semidirect products: an effective characterization of the until hierarchy
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Alternating automata and the temporal logic of ordinals
Alternating automata and the temporal logic of ordinals
The stuttering principle revisited
Acta Informatica
Reasoning about infinite computation paths
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Characteristic patterns for LTL
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
From LTL to symbolically represented deterministic automata
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
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It is known that Linear Temporal Logic (LTL) has the same expressive power as alternating 1-weak automata (A1W automata, also called alternating linear automata or very weak alternating automata). A translation of LTL formulae into a language equivalent A1W automata has been introduced in [1]. The inverse translation has been developed independently in [2] and [3]. In the first part of the paper we show that the latter translation wastes temporal operators and we propose some improvements of this translation. The second part of the paper draws a direct connection between fragments of the Until-Release hierarchy [4] and alternation depth of nonaccepting and accepting states in A1W automata. We also indicate some corollaries and applications of these results.