Semirings, automata, languages
Semirings, automata, languages
Rational series and their languages
Rational series and their languages
A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
Digital images and formal languages
Handbook of formal languages, vol. 3
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
The consensus string problem and the complexity of comparing hidden Markov models
Journal of Computer and System Sciences - Computational biology 2002
Semiring frameworks and algorithms for shortest-distance problems
Journal of Automata, Languages and Combinatorics
Clique Is Hard to Approximate within n1-o(1)
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Finite-state transducers in language and speech processing
Computational Linguistics
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Efficient computation of the relative entropy of probabilistic automata
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Computation of distances for regular and context-free probabilistic languages
Theoretical Computer Science
Absolute Convergence of Rational Series Is Semi-decidable
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Absolute convergence of rational series is semi-decidable
Information and Computation
Language equivalence for probabilistic automata
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Finding the most probable string and the consensus string: an algorithmic study
IWPT '11 Proceedings of the 12th International Conference on Parsing Technologies
On the complexity of the equivalence problem for probabilistic automata
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
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The problem of the computation of a distance between two probabilistic automata arises in a variety of statistical learning problems. This paper presents an exhaustive analysis of the problem of computing the Lp distance between two automata. We give efficient exact and approximate algorithms for computing these distances for p even and prove the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. We also give an efficient algorithm for computing the Hellinger distance between unambiguous probabilistic automata. Our results include a general algorithm for the computation of the norm of an unambiguous probabilistic automaton based on a monoid morphism and efficient algorithms for the specific case of the computation of the Lp norm. Finally, we also describe an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A1 and A2 based on Schützenberger’s standardization with a running time complexity of O(|Σ| (|A1| + |A2|)3), a significant improvement over the previously best algorithm reported for this problem.