Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Principles of Program Analysis
Principles of Program Analysis
Conditional Context-Free Languages of Finite Index
New Trends in Formal Languages - Control, Cooperation, and Combinatorics (to Jürgen Dassow on the occasion of his 50th birthday)
Parikh's Theorem in Commutative Kleene Algebra
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
On the convergence of Newton's method for monotone systems of polynomial equations
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximative Methods for Monotone Systems of Min-Max-Polynomial Equations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Journal of Computer and System Sciences
On fixed point equations over commutative semirings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
An extension of Newton's method to ω-continuous semirings
DLT'07 Proceedings of the 11th international conference on Developments in language theory
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
Interprocedural Dataflow Analysis over Weight Domains with Infinite Descending Chains
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Solving fixed-point equations by derivation tree analysis
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Weighted dynamic pushdown networks
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Formal Methods in System Design
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Fixed point equations ${\bf\it X} = {\bf\it f}({\bf\it X})$ over¿-continuous semirings are a natural mathematicalfoundation of interprocedural program analysis. Generic algorithmsfor solving these equations are based on Kleene's theorem, whichstates that the sequence ${\bf{0}}, {\bf\it f}({\bf{0}}), {\bf\itf}({\bf\it f}({\bf{0}})), \ldots$ converges to the least fixedpoint. However, this approach is often inefficient. We report onrecent work in which we extend Newton's method, the well-knowntechnique from numerical mathematics, to arbitraryω-continuous semirings, and analyze its convergencespeed in the real semiring.