Polynomial space counting problems
SIAM Journal on Computing
Deciding equivalence of finite tree automata
SIAM Journal on Computing
A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
Languages, automata, and logic
Handbook of formal languages, vol. 3
The Equality Problem for Rational Series with Multiplicities in the Tropical Semiring is Undecidable
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton
Theoretical Computer Science - Developments in language theory
Weighted automata and weighted logics
Theoretical Computer Science
Weighted versus Probabilistic Logics
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Elements of Automata Theory
Handbook of Weighted Automata
ACM Transactions on Computational Logic (TOCL)
Pebble weighted automata and transitive closure logics
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Regular Cost Functions over Finite Trees
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
What's decidable about weighted automata?
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Rigorous Approximated Determinization of Weighted Automata
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Temporal Specifications with Accumulative Values
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Weighted automata and weighted MSO logics for average and long-time behaviors
Information and Computation
Adding pebbles to weighted automata
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Hi-index | 0.00 |
While monadic second-order logic is a prominent logic for specifying languages of finite words, it lacks the power to compute quantitative properties, e.g. to count. An automata model capable of computing such properties are weighted automata, but logics equivalent to these automata have only recently emerged. We propose a new framework for adding quantitative properties to logics specifying Boolean properties of words. We use this to define Quantitative Monadic Second-Order Logic (QMSO). In this way we obtain a simple logic which is equally expressive to weighted automata. We analyse its evaluation complexity, both data and combined complexity, and show completeness results for combined complexity. We further refine the analysis of this logic and obtain fragments that characterise exactly subclasses of weighted automata defined by the level of ambiguity allowed in the automata. In this way, we define a quantitative logic which has good decidability properties while being resonably expressive and enjoying a simple syntactical definition.