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Abstract. The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation algorithms can be developed to exploit the structure of particular constraints, much as is done for domain filtering algorithms. We propose specialized propagation algorithms for alldiff and inequality constraints. Preliminary experiments show that MDD propagation solves multiple alldiff problems an order of magnitude more rapidly than traditional domain propagation. It also significantly reduces the search tree for inequality problems, but additional research is needed to reduce the computation time.

Abstract

This paper describes a new data structure, difference decision diagrams (DDDs)

This paper describes a method for translating a satisfaction problem of the modal p-calculus into a problem of finding a certain marking of a boolean graph. By giving algorithms to solve the graph problem, we present a global model checking algorithm for the modal p-calculus of alternation depth one, which has time-complexity ]AIIT h where IAI is the size of the assertion and IT] is the size of the model (a labelled transition system). This algorithm extends to an algorithm for the full modal p-calculus which runs in time (IAI]TI) ad, where ad is the alternation depth, improving on earlier presented algorithms. Moreover, a local algorithm is presented for alternation depth one, which runs in time IAIIT] log(IAIITI) , improving on the earlier published algorithms that are all at least exponential. *This work is supported by the ESPRIT Basic Research Action CEDISYS and by the Danish Natural Science Research Council. monotone function on a boolean lattice consisting of a product of simple two-point lattices. Secondly, it is shown how this fixed-point can be found in linear time using a simple graph algorithm, thereby giving an IAI ITI model checking algorithm. Thirdly, this algorithm will be extended to the full calculus, giving an algorithm running in time (IAIIT I) ,a, ad being the alternation depth-a measure of how intertwined minimal and maximal fixed-points are. Finally, a local algorithm, searching potentially only a part of the transition system, will be presented for the modal #-calculus of alternation depth one. This algorithm will run in time ]A[[T I log(IA]lTI). Related work can be found in Emerson and Lei [EL86] which describes an ([A[ IT]) "a+a algorithm and defines the notion of alternation depth, in Arnold and Crubille [AC88] which describes an IA[21TI algorithm for the case of one simultaneous fixed-point, in Cleaveland and Stirling [CS91] which describes an ]AI]T ] algorithm for alternation depth one, and finally in Larsen [Lar88], Stirling and Walker [SW89], Cleaveland [Cle90], and Winskel [Win89] which all describe local model checkers that are at least exponentialeven for alternation depth one.