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On Determining the AND-OR Hierarchy in Workflow Nets

100%

Sroka J. , Hidders J.

tom Vol. 156, nr 1

95--123

This paper presents a notion of reduction where a WF net is transformed into a smaller net by iteratively contracting certain well-formed subnets into single nodes until no more of such contractions are possible. This reduction can reveal the hierarchical structure of a WF net, and since it preserves certain semantic properties such as soundness, can help with analysing and understanding why a WF net is sound or not. The reduction can also be used to verify if a WF net is an AND-OR net. This class of WF nets was introduced in earlier work, and arguably describes nets that follow good hierarchical design principles. It is shown that the reduction is confluent up to isomorphism, which means that despite the inherent non-determinism that comes from the choice of subnets that are contracted, the final result of the reduction is always the same up to the choice of the identity of the nodes. Based on this result, a polynomial-time algorithm is presented that computes this unique result of the reduction. Finally, it is shown how this algorithm can be used to verify if a WF net is an AND-OR net.

On Banach spaces of regulated functions

72%

Drewnowski L.

tom Vol 57, No. 2

153--169

For a relatively compact subset S of the real line R, let R(S) denote the Banach space (under the sup norm) of all regulated scalar functions defined on S. The purpose of this paper is to study those closed subspaces of R(S) that consist of functions that are left-continuous, right-continuous, continuous, and have a (two-sided) limit at each point of some specified disjoint subsets of S. In particular, some of these spaces are represented as C(K) spaces for suitable, explicitly constructed, compact spaces K.