Complexity of pattern-based verification for multithreaded programs
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Efficient reasoning about data trees via integer linear programming
Proceedings of the 14th International Conference on Database Theory
Parikh's theorem: A simple and direct automaton construction
Information Processing Letters
The complexity of reversal-bounded model-checking
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Parikh's theorem and descriptional complexity
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Efficient reasoning about data trees via integer linear programming
ACM Transactions on Database Systems (TODS)
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
On selective unboundedness of VASS
Journal of Computer and System Sciences
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Parikh’s Theorem states that semilinear sets are effectively equivalent with the Parikh images of regular languages and those of context-free languages. In this paper, we study the complexity of Parikh’s Theorem over any fixed alphabet size d. We prove various normal form the oremsin the case of NFAs and CFGs. In particular, the normalform theorems ensure that a union of linear sets with dgenerators suffice to express such Parikh images, which in the case of NFAs can further be computed in polynomial time. We then apply apply our results to derive: (1) optimal complexity for decision problems concerning Parikh images(e.g. membership, universality, equivalence, and disjointness), (2) a new polynomial fragment of integer programming, (3) an answer to an open question about PAC-learnability of semilinear sets, and (4) an optimal algorithm for verifying LTL over discrete-timed reversal-bounded counter systems.