A generic approach to the static analysis of concurrent programs with procedures
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Equational Theory of Fixed Points with Applications to Generalized Language Theory
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Greibach Normal Form in Algebraically Complete Semirings
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
An Algebraic Approach to the Static Analysis of Concurrent Software
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Combining Equational Tree Automata over AC and ACI Theories
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Newton's Method for ω-Continuous Semirings
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Derivation Tree Analysis for Accelerated Fixed-Point Computation
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
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
Reachability Analysis of Synchronized PA Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Efficient computation of throughput values of context-free languages
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
The algebraic approach I: the algebraization of the chomsky hierarchy
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Journal of the ACM (JACM)
Parikh's theorem: A simple and direct automaton construction
Information Processing Letters
An appreciation of dexter kozen
Logic and Program Semantics
Path algorithms on regular graphs
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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Parikh's Theorem says that the commutative image of every context free language is the commutative image of some regular set. Pilling has shown that this theorem is essentially a statement about least solutions of polynomial inequalities. We prove the following general theorem of commutative Kleene algebra, of which Parikh's theorem is a special case: Every system of polynomial inequalities fi(x1,...,xn) \mathxi, 1 \mathi \math, over a commutative Kleene algebra K has a unique least solution in Kn; moreover, the components of the solution are given by polynomials in the coefficients of the fi. We also give a closed-form solution in terms of the Jacobian of the system.