Principles of Program Analysis
Principles of Program Analysis
On-the-Fly Analysis of Systems with Unbounded, Lossy FIFO Channels
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Parikh's Theorem in Commutative Kleene Algebra
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Weighted pushdown systems and their application to interprocedural dataflow analysis
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
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
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
Using bisimulations for optimality problems in model refinement
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Solving fixed-point equations by derivation tree analysis
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
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We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations is equal to the least fixed-point of a linearsystem obtained by "linearizing" the polynomials of in a certain way. Our proofs rely on derivation tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in [5] to show that Newton's method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of [2]), and a generalization of Courcelle's result stating that the downward-closed image of a context-free language is regular [3].