Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Random walks with “back buttons” (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Quantitative Analysis of Probabilistic Pushdown Automata: Expectations and Variances
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Checking LTL Properties of Recursive Markov Chains
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Journal of the ACM (JACM)
On fixed point equations over commutative semirings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Algorithmic verification of recursive probabilistic state machines
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Newton's Method for ω-Continuous Semirings
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Automata, Probability, and Recursion
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Journal of the ACM (JACM)
Discounted Properties of Probabilistic Pushdown Automata
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Parsing algorithms based on tree automata
IWPT '09 Proceedings of the 11th International Conference on Parsing Technologies
On least fixed points of systems of positive polynomials
ACM Communications in Computer Algebra
Journal of the ACM (JACM)
Space-efficient scheduling of stochastically generated tasks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Computing the Least Fixed Point of Positive Polynomial Systems
SIAM Journal on Computing
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Prefix probability for probabilistic synchronous context-free grammars
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
Runtime analysis of probabilistic programs with unbounded recursion
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Efficient analysis of probabilistic programs with an unbounded counter
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Space-efficient scheduling of stochastically generated tasks
Information and Computation
On Buffon machines and numbers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Computation of infix probabilities for probabilistic context-free grammars
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Prefix probabilities for linear context-free rewriting systems
IWPT '11 Proceedings of the 12th International Conference on Parsing Technologies
Analyzing probabilistic pushdown automata
Formal Methods in System Design
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Monotone systems of polynomial equations (MSPEs) are systems of fixed-point equations X1 = f1(X1, ..., Xn), ..., Xn = fn(X1, ..., Xn) where each fi is a polynomial with positive real coefficients. The question of computing the least non-negative solution of a given MSPE X = f(X) arises naturally in the analysis of stochastic context-free grammars, recursive Markov chains, and probabilistic pushdown automata. While the Kleene sequence f(0), f(f(0)), ... always converges to the least solution mu.f, if it exists, the number of iterations needed to compute the first i bits of mu.f may grow exponentially in i.Etessami and Yannakakis have recently adapted Newton's iterative method to MSPEs and proved that the Newton sequence converges at least as fast as the Kleene sequence and exponentially faster in many cases.They conjecture that, given an MSPE of size m, the number of Newton iterations needed to obtain i accurate bits of mu.f grows polynomially in i and m. In this paper we show that the number of iterations grows linearly in i for strongly connected MSPEs and may grow exponentially in m for general MSPEs.