FIRST-ORDER AND TEMPORAL LOGICS FOR NESTED WORDS
Publication Date
2008
Journal or Book Title
LOGICAL METHODS IN COMPUTER SCIENCE
Abstract
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide new temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a "within" modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.
DOI
http://dx.doi.org/10.2168/LMCS-4(4:11)2008
Pages
-
Volume
4
Issue
4
Recommended Citation
Alur, R; Arenas, M; Barcelo, P; Etessami, K; Immerman, N; and Libkin, L, "FIRST-ORDER AND TEMPORAL LOGICS FOR NESTED WORDS" (2008). LOGICAL METHODS IN COMPUTER SCIENCE. 556.
http://dx.doi.org/10.2168/LMCS-4(4:11)2008