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
Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa
On the Power of Tree-Walking Automata
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Weighted automata and weighted logics
Theoretical Computer Science
XPath, transitive closure logic, and nested tree walking automata
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Language and Automata Theory and Applications
Handbook of Weighted Automata
Weighted tree-walking automata
Acta Cybernetica
Expressive power of pebble automata
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Complexity of pebble tree-walking automata
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Adding pebbles to weighted automata
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
A probabilistic kleene theorem
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Weighted specifications over nested words
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Quantitative Monadic Second-Order Logic
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We introduce new classes of weighted automata on words. Equipped with pebbles and a two-way mechanism, they go beyond the class of recognizable formal power series, but capture a weighted version of first-order logic with bounded transitive closure. In contrast to previous work, this logic allows for unrestricted use of universal quantification. Our main result states that pebble weighted automata, nested weighted automata, and this weighted logic are expressively equivalent. We also give new logical characterizations of the recognizable series.