Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree
14th International Colloquium on Automata, languages and programming
Handbook of theoretical computer science (vol. B)
An Until hierarchy and other applications of an Ehrenfeucht-Fraïssé game for temporal logic
Information and Computation - Special issue: LICS 1996—Part 1
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
First-Order Logic on Finite Trees
TAPSOFT '95 Proceedings of the 6th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Expressive Power of Temporal Logics
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
On the Expressive Power of CTL
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Conditional XPath, the first order complete XPath dialect
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Temporal Logics over Unranked Trees
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2004
Effective characterizations of tree logics
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient and expressive tree filters
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
First order paths in ordered trees
ICDT'05 Proceedings of the 10th international conference on Database Theory
Datalog relaunched: simulation unification and value invention
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Early nested word automata for XPath query answering on XML streams
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
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Marx and de Rijke have shown that the navigational core of the w3c XML query language XPath is not first-order complete -- that is it cannot express every query definable in firstorder logic over the navigational predicates. How can one extend XPath to get a first-order complete language? Marx has shown that Conditional XPath -- an extension of XPath with an "Until" operator -- is first order complete. The completeness argument makes essential use of the presence of upward axes in Conditional XPath. We examine whether it is possible to get "forward-only" languages that are first-order complete for XML Boolean queries. It is easy to see that a variant of the temporal logic CTL* is first-order complete; the variant has path quantifiers for downward, leftward and rightward paths, while along a path one can check arbitrary formulas of linear temporal logic (LTL). This language has two major disadvantages: it requires path quantification in both horizontal directions (in particular, it requires looking backward at the prior siblings of a node), and it requires the consideration of formulas of LTL of arbitrary complexity on vertical paths. This last is in contrast with Marx's Conditional XPath, which requires only the checking of a single Until operator on a path. We investigate whether either of these restrictions can be eliminated. Our main results are negative ones. We show that if we restrict our CTL* language by having an until operator in only one horizontal direction, then we lose completeness. We also show that no restriction to a "small" subset of LTL along vertical paths is sufficient for first order completeness. Smallness here means of bounded "Until Depth", a measure of complexity of LTL formulas defined by Etessami and Wilke. In particular, it follows from our work that Conditional XPath with only forward axes is not expressively complete; this extends results proved by Rabinovich and Maoz in the context of infinite unordered trees.