The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Definability with bounded number of bound variables
Information and Computation
Handbook of theoretical computer science (vol. B)
Reasoning in a restricted temporal logic
Information and Computation
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Temporal Logic and Semidirect Products: An Effective Characterization of the Until Hierarchy
SIAM Journal on Computing
Proceedings of the First International Conference on Temporal Logic
ICTL '94 Proceedings of the First International Conference on Temporal Logic
On the Ehrenfeucht-Fraïssé Game in Theoretical Computer Science
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An infinite hierarchy of temporal logics over branching time
Information and Computation
An Expressive Extension of TLC
ASIAN '99 Proceedings of the 5th Asian Computing Science Conference on Advances in Computing Science
Nesting Until and Since in Linear Temporal Logic
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
A note on the characterization of TL[EF]
Information Processing Letters
On First-Order Fragments for Mazurkiewicz Traces
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Games for Temporal Logics on Trees
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
A note on the expressibility problem for modal logics and star-free regular expressions
Information Processing Letters
Classifying discrete temporal properties
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the expressiveness of MTL variants over dense time
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
A theory of sampling for continuous-time metric temporal logic
ACM Transactions on Computational Logic (TOCL)
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
On First-Order Fragments for Mazurkiewicz Traces
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
VeriDroid: automating Android application verification
Proceedings of the 2013 Middleware Doctoral Symposium
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We prove there is a strict hierarchy of expressive power according to the Until depth of linear temporal logic (TL) formulas: for each k, there is a very natural property that is not expressible with k nestings of Until operators, regardless of the number of applications of other operators, but is expressible by a formula with Until depth k+1. Our proof uses a new Ehrenfeucht-Frai}sse (EF) game designed specifically for TL. These properties can all be expressed in first-order logic with quantifier depth and size O(log k), and we use them to observe some interesting relationships between TL and first-order expressibility. We then use the EF game in a novel way to effectively characterize (1) the TL properties expressible without Until, as well as (2) those expressible without both Until and Next. By playing the game ``on finite automata'', we prove that the automata recognizing languages expressible in each of the two fragments have distinctive structural properties. The characterization for the first fragment was originally proven by Cohen, Perrin, and Pin using sophisticated semigroup-theoretic techniques. They asked whether such a characterization exists for the second fragment. The technique we develop is general and can potentially be applied in other contexts.