# On the Complexity of Linear and Stratified : Context Matching Problems

1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We give algorithms for linear and for general context matching and discuss how the performance in the general case can be improved through the use of information derived from approximations that can be computed in polynomial time. We investigate the complexity of context matching with respect to the stratification of variable occurrences, where our main results are that stratified context matching is NP-complete, but that stratified simultaneous monadic context matching is in P. SSMCM is equivalent to stratified simultaneous word matching. We also show that the linear and the shared-linear case are in P and of time complexity $O(n^3)$, and that varity 2 context matching, where variables occur at most twice, is NP-complete.
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https://hal.inria.fr/inria-00071656
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 6:24:44 PM
Last modification on : Thursday, January 11, 2018 - 6:19:58 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:31:43 PM

### Identifiers

• HAL Id : inria-00071656, version 1

### Citation

Manfred Schmidt-Schauss, Jürgen Stuber. On the Complexity of Linear and Stratified : Context Matching Problems. [Research Report] RR-4923, INRIA. 2003, pp.28. ⟨inria-00071656⟩

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