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Abstract: We introduce a new Ehrenfeucht-Fra ss e game for proving lower bounds on the size of first-order formulas. Up until now such games have only been used to prove bounds on the operator depth of formulas, not their size. We use this game to prove that the CTL + formula Occurn # E[Fp 1 # Fp 2 # # Fpn ] which says that there is a path along which the predicates p 1 through pn occur in some order, requires size n! to express in CTL. Our lower bound is optimal. It follows that the succinctness ... (Update)
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BibTeX entry: (Update)
M. Adler and N. Immerman. An n! lower bound on formula size. Manuscript, 1999. http://citeseer.ist.psu.edu/adler99lower.html More
@inproceedings{ adler01lower,
author = "Micah Adler and Neil Immerman",
title = "An n! Lower Bound on Formula Size",
booktitle = "Logic in Computer Science",
pages = "197-",
year = "2001",
url = "citeseer.ist.psu.edu/adler99lower.html" }
Citations (may not include all citations):397 Design and Synthesis of Synchronization Skeletons Using Bran.. (context) - Clarke, Emerson - 1981
222 The Complexity of Propositional Linear Temporal Logics (context) - Sistla, Clarke - 1985
211 Languages that capture complexity classes - Immerman - 1987
115 An Application of Games to the Completeness Problem for Form.. (context) - Ehrenfeucht - 1961
84 Decision Procedures and Expressiveness in the Temporal Logic.. (context) - Emerson, Halpern - 1985
29 An Until Hierarchy for Temporal Logic - Etessami, Wilke - 1996
23 Model Checking and Transitive Closure Logic - Immerman, Vardi - 1997
22 Grumberg and D (context) - Clarke - 1999
13 Communication Complexity: A New Approach to Circuit Depth (context) - Karchmer - 1989
9 Springer Graduate Texts in Computer Science (context) - Immerman, Complexity - 1999
7 Tree Canonization and Transitive Closure - Etessami, Immerman - 1995
3 Reachability Logic: An Efficient Fragment of Transitive Clos.. - Alechina, Immerman - 2000
1 CTL + is Exponentially More Succinct than CTL - Wilke - 1999
1 Sur les Classifications des Systems de Relations (context) - Frasse - 1954
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