Abstract
The paper presents a general algorithm for computing nested fix-points over complete lattices of finite height. The method presented relies on techniques familiar from the realm of functional programming languages, such as e.g. lazy evaluation. The algorithm is constructed in a stepwise fashion: We start with a schema based on some simple facts of fix-point theory. As such this schema is easily seen to be correct. It is, however, rather inefficient. We then trace the sources of inefficiency and refine the basic schema resulting in a correct and more efficient algorithm. After presenting the general algorithm, we apply it, by means of illustration, to the field of model checking.
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Andersen, H. R.: Model Checking and Boolean Graphs, ESOP'92, LNCS 582, 1992
Andersen, H. R.: Verification of Temporal Properties of Concurrent Systems, PhD thesis, Aarhus University, DAIMI PB — 445, 1993
Arnold, A., Crubille, P.: A linear algorithm to solve fixed-points equations on transition systems, Information Processing Letters, vol.29, 57–66, 1988
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications, ACM Transactions on Progr. Languages and Systems, Vol.8, No. 2, pp. 244–263, April 1986
Cleaveland, R.: Tableau-based model checking in the propositional mucalculus, Acta Informatica, 1990
Cleaveland, R., Klein, M., Steffen, B.: Faster Model Checking for the Modal MuCalculus, CAV'92, LNCS 663
Cleaveland, R., Steffen, B.: Computing Behavioural Relations, Logically, ICALP 91, pp. 127–138, LNCS 510
Cleaveland, R. and Steffen, B.: A Linear-Time Model-Checking Algorithm for the Alternation-Free Modal Mu-Calculus, CAV'91, LNCS 575, 1992
Emerson, E.A., Lei, C.-L.: Efficient model checking in fragments of the propositional μ-calculus, LICS, 267–278, 1986
Kozen, D.: Results on the propositional mu-calculus, TCS 17, 1983
Larsen, K.G.: Efficient Local Correctness Checking, CAV'92, LNCS 663
Larsen, K.G.: Proof systems for Hennessy-Milner logic with recursion, CAAP, 1988, see also TCS, 72, 1990
Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification, (Proc.) 12th ACM annual Symposium on Principles of Programming Languages, pp. 97–107, 1985
Stirling, C., Walker, D.: Local model checking in the modal mu-calculus, TCS, October 1991, see also LNCS 351, 369–383, CAAP 1989
Stirling, C.: Modal and Temporal Logics, in Handbook of Logic in Computer Sciences, Volume 2. Edited by S. Abramsky, M. Gabbay and T.S.E. Maibaum; Oxford Science Publications, 1992
Tarski, A.: A Lattice-Theoretical Fixpoint Theorem and its Applications, Pacific Journal of Mathematics, 5: 285–309, 1955
Vergauwen, B., Lewi, J.: A linear algorithm for solving fixed points equations on transition systems, CAAP'92, LNCS 581, 322–341
Vergauwen, B., Lewi, J.: A Linear Local Model Checking Algorithm for CTL, CONCUR'93, LNCS 715
Winskel, G.: A note on model checking the modal nu-calculus, ICALP, LNCS 372, 1989, see also TCS 83, 1991
Xinxin, L.: Specification and Decomposition in Concurrency, PhD thesis, Aalborg University, 1992, R 92-2005
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© 1994 Springer-Verlag Berlin Heidelberg
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Vergauwen, B., Lewi, J., Avau, I., Poté, A. (1994). Efficient computation of nested fix-points, with applications to model checking. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013987
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DOI: https://doi.org/10.1007/BFb0013987
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