Theoretical Computer Science
On a monadic NP vs monadic co-NP
Information and Computation
Complexity results for two-way and multi-pebble automata and their logics
ICALP '94 Selected papers from the 21st international colloquium on Automata, languages and programming
A logical characterization of data languages
Information Processing Letters
Finite state machines for strings over infinite alphabets
ACM Transactions on Computational Logic (TOCL)
On the freeze quantifier in Constraint LTL: Decidability and complexity
Information and Computation
LTL with the freeze quantifier and register automata
ACM Transactions on Computational Logic (TOCL)
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
On pebble automata for data languages with decidable emptiness problem
Journal of Computer and System Sciences
Safety alternating automata on data words
ACM Transactions on Computational Logic (TOCL)
Two-variable logic on data words
ACM Transactions on Computational Logic (TOCL)
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Automata and logics for words and trees over an infinite alphabet
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
On notions of regularity for data languages
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a0b0a1b1 ⋯ anbn of even length over D can be viewed as a directed graph Gw whose vertices are the symbols that appear in w, and the edges are (a0, b0), (a1, b1), ..., (an, bn). For a positive integer m, define a language Rm such that a word w = a0b0 ⋯ anbn ∈ Rm if and only if there is a path in the graph Gw of length ≤ m from the vertex a0 to the vertex bn. We establish the following hierarchy theorem for pebble automata over infinite alphabet. For every positive integer k, (i) there exists a k-pebble automaton that accepts the language R2k − 1; (ii) there is no k-pebble automaton that accepts the language R2k + 1 − 2. Using this fact, we establish the following main results in this article: (a) a strict hierarchy of the pebble automata languages based on the number of pebbles; (b) the separation of monadic second order logic from the pebble automata languages; (c) the separation of one-way deterministic register automata languages from pebble automata languages.