V. Gupta. Concurrent kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, Ithaca, August 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and situation predicates. The corresponding relation RS contains all pairs of worlds that are members of this set. The relation R serves as the basis for PSL ordering operators. This relation is simplest to describe formally when expressions are restricted to event predicates on fixed messages [24, 70, 58]. In this case, expressions in V are just characteristic predicates of sets of event occurrences, and OE(e,w) is true if w contains the events of e. For example, suppose a satisfies e a = out(m1) for some message m1, and b satisfies e b = out(m1) in(m1) The relation a b states that e b ) e ....

....in a simple way under the intended mapping to raw events: If the instances of two events are ordered, then so are the corresponding instances of event predicates. PSL operators, situations, and partitionings are more closely related to corresponding constructs in event structures and its variants [70, 24, 58], as adapted for use in interface based specification. 7 Appendix Here we describe relations between PSL IDL conventions and underlying PSL constructs. We first introduce an expanded notation for representing situations as named, parameterized predicates of the form Name(Parameters) ....

Gupta, V., "Concurrent Kripke Structures", Proceedings of the North American Process Algebra Workshop Cornell CS-TR-93-1369, 1993.

....something of a jigsaw puzzle. One is then naturally led to ask whether the pieces of this puzzle can be arranged in some recognizable order. In this paper we review the outcome to date of our recent investigations of Chu spaces as a candidate unifying framework for these aspects of concurrency [Pra92, Pra93, Gup93, GP93, Gup94, Pra94b, Pra95a]. Their simplicity is deceptive, and two years of experience with them have convinced us that they are more than adequately equipped for this role. Chu spaces are simple, useful, and well organized. With regard to simplicity, a Chu space is merely a matrix that transforms by deleting and copying ....

V. Gupta. Concurrent Kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

....for this particular organization, as well as the language of this metadiscussion, all these operations are definable in traditional set theoretic terms. Chu spaces first entered our investigations of the nature of concurrent computation in June of 1992 when we found with our student V. Gupta [Gup93, GP93, Gup94] that they captured exactly the notion of partial distributive lattice that we had been trying to pin down [Pra92d] as an extension of our earlier notion of event space [Pra92c, Pra92a, Pra92b] More recently [Pra95] we have arrived at the view of =j and its converse j= as the dual relations of ....

V. Gupta. Concurrent Kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

....notions of enabling and conflict. What was not changed there was the 2 valued logic of configuration structures, the net effect then being to make their notion of general configuration structure equivalent to the extensional Chu spaces over 2 studied by Gupta and Pratt as a model of concurrency [Gup93, GP93, Gup94]. Our use of the above three element quantale will turn out to be equivalent to using Chu spaces over 3, unexpectedly with no mention made by the latter concerning that choice of quantale. This solves the basic problem in full, at least to the extent defined by its formulation above. For HDA s, ....

V. Gupta. Concurrent Kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

.... row and column are interchanged everywhere, dealing immediately with the case of projection onto the time axis, yielding a schedule. That these objects are recognizable automata and schedules respectively (with loops and disjunctive confluences unfolded) can be appreciated from the examples in [Gup93, GP93, Pra93b, Gup94, Pra94a]. 6.4 Universality of Chu Spaces The categories Str of ary relational structures and their homomorphisms where is any ordinal are universal categories for mathematics to the extent that they realize many familiar categories: groups, lattices, and Boolean algebras when = 3, rings, fields, and ....

V. Gupta. Concurrent kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

....theorem, simple semigroups are in 1 1 correspondence with functions Y Theta X H . Such functions form the basis of a new approach to foundations of concurrency and foundations of computer science in general which is promoted by V. R. Pratt from Stanford under the name of Chu spaces (see, e. g, [5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]) Thus, a general extension of t norms naturally leads us to Chu spaces. Auxiliary Results and Their Relationship With the Existence and Borderline Character of Classical Truth Values. According to [1] Theorem 1.8, and [11] Theorem 1.4.2, if a compact topological semigroup S is not a group ....

V. Gupta, "Concurrent Kripke Structures", In: Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

....their interaction, and matrix transposition is the duality interchanging mind and body to yield the dual Chu space A = X; A; j= Points have necessary existence, all being present simultaneously in the physical object A. States are possible, making a Chu space a kind of a Kripke structure [Gup93]: only one state at a time may be chosen from the menu X of alternatives. Lafont and Streicher [LS91] were the first to single out Chu spaces as a case of the more general Chu construction Chu(V; k) Bar79, Bar91] namely V = Set, worthy of separate attention as a natural model of linear logic ....

V. Gupta. Concurrent Kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

..... other authors have used all sorts of weird combinations for writing it in L aT E X ) The work in chapter 6 has also benefited from discussions with Dr. R. J. van Glabbeek and Prof. Gordon D. Plotkin. Some of the results in the thesis have been published in [Gup93, GP93]. Chapter 2 Models of Concurrency Before we get into Chu space theory and applications we will briefly review some models of concurrency which contributed ideas to our model. These include Petri nets, traces, transition graphs and CCS, event structures, geometric automata and pomsets. All models ....

V. Gupta. Concurrent kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, August 1993.

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V. Gupta. Concurrent kripke structures. In Proceedings of the North American Process Algebra Workshop, Cornell CS-TR-93-1369, Ithaca, August 1993.

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