On Guarding Nested Fixpoints
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For every hierarchicalsystem of equations S over some complete and distributive lattice we construct an equivalent system with the same set of variables which additionally is guarded. The price to be paid is that the resulting right-hand sides may grow exponentially. We therefore present methods how the exponentialbl ow-up can be avoided. Especially, the loop structure of the variable dependence graph is taken into account. Also we prove that size O(m· S) suffices whenever S originates from a fixpoint expression where the nesting-depth of fixpoints is at most m. Finally, we sketch an application to regular tree pattern-matching.
KeywordsDistributive Lattice Free Variable Complete Lattice Hierarchical System Variable Assignment
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- 1.H.R. Andersen, C. Stirling, and G. Winskel. A Compositional Proof System for the Modal Mu-Calculus. In IEEE Conf. on Logic in Computer Science (LICS), 144–153, 1994.Google Scholar
- 3.H. Bekic. Definable Operations in General Algebras, and the Theory of Automata and Flowcharts. Technical Report, IBM Labor, Wien, 1967.Google Scholar
- 6.C. Fecht and H. Seidl. A Faster Solver for General Systems of Equations. Science of Computer Programming (SCP), 1999. To appear.Google Scholar
- 8.M.S. Hecht. Flow Analysis of Computer Programs. North Holland, 1977.Google Scholar
- 11.R. Kaivola. Using Automata to Characterise Fixpoint Temporal Logics. PhD thesis, Dept. of Computer Science, Univ. of Edinburgh, 1996.Google Scholar
- 14.A. Mader. Verification of Modal Properties Using Boolean Equation Systems. PhD thesis, TU München, 1997.Google Scholar
- 18.H. Seidland D. Niwinski. On Distributive Fixpoint Expressions. TechnicalRep ort TR 98-04 (253), University of Warsaw, 1998. To appear in RAIRO.Google Scholar
- 20.I. Walukiewicz. Notes on the Propositional μ-Calculus: Completeness and Related Results. Technical Report NS-95-1, BRICS Notes Series, 1995.Google Scholar