A taxonomy of problems with fast parallel algorithms
Information and Control
A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
On path equivalence of nondeterministic finite automata
Information Processing Letters
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Deciding DPDA Equivalence Is Primitive Recursive
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The Equivalence Problem for Deterministic Pushdown Automata is Decidable
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On probabilistic program equivalence and refinement
CONCUR 2005 - Concurrency Theory
On the complexity of space bounded interactive proofs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Journal of the ACM (JACM)
Remote timing attacks are practical
Computer Networks: The International Journal of Computer and Telecommunications Networking - Web security
On the Complexity of Numerical Analysis
SIAM Journal on Computing
On automated verification of probabilistic programs
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Language equivalence for probabilistic automata
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
What's decidable about weighted automata?
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
On the computation of some standard distances between probabilistic automata
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
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
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
Decidability of DPDA Language Equivalence via First-Order Grammars
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
A probabilistic kleene theorem
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
PRINSYS: on a quest for probabilistic loop invariants
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
Hi-index | 0.00 |
Deciding equivalence of probabilistic automata is a key problem for establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this paper we show that polynomial identity testing yields efficient algorithms for various generalisations of the equivalence problem. First, we provide a randomized NC procedure that also outputs a counterexample trace in case of inequivalence. Second, we consider equivalence of probabilistic cost automata. In these automata transitions are labelled with integer costs and each word is associated with a distribution on costs, corresponding to the cumulative costs of the accepting runs on that word. Two automata are equivalent if they induce the same cost distributions on each input word. We show that equivalence can be checked in randomised polynomial time. Finally we show that the equivalence problem for probabilistic visibly pushdown automata is logspace equivalent to the problem of whether a polynomial represented by an arithmetic circuit is identically zero.