Decision procedures and expressiveness in the temporal logic of branching time
Journal of Computer and System Sciences
The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Temporal logic of programs
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Branching time and partial order in temporal logics
Time and logic
The Complexity of Tree Automata and Logics of Programs
SIAM Journal on Computing
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Focus Games for Satisfiability and Completeness of Temporal Logic
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Temporal Logic and State Systems (Texts in Theoretical Computer Science. An EATCS Series)
Temporal Logic and State Systems (Texts in Theoretical Computer Science. An EATCS Series)
Information and Computation
CTL+ is complete for double exponential time
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A decision procedure for CTL* based on tableaux and automata
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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The full branching time logic ctl* is a well-known specification logic for reactive systems. Its satisfiability and model checking problems are well understood. However, it is still lacking a satisfactory sound and complete axiomatisation. The only proof system known for ctl* is Reynolds' which comes with an intricate and long completeness proof and, most of all, uses rules that do not possess the subformula property. In this paper we consider a large fragment of ctl* which is characterised by disallowing certain nestings of temporal operators inside universal path quantifiers. This subsumes ctl+ for instance. We present infinite satisfiability games for this fragment. Winning strategies for one of the players represent infinite tree models for satisfiable formulas. These can be pruned into finite trees using fixpoint strengthening and some simple combinatorial machinery such that the results represent proofs in a Hilbert-style axiom system for this fragment. Completeness of this axiomatisation is a simple consequence of soundness of the satisfiability games.