Pratt, V., Chu spaces: Automata with quantum aspects, Technical report, Stanford University (1994).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the square as well as its boundary. Adding in the model the concept interior of a square (as well as interior of any n cube when we model n concurrent processes in parallel) naturally leads to the notion of precubical set. 5 Which, later, will also motivate the introduction of Chu spaces [50]. Homology, Homotopy and Applications, vol. No. 2001 10 a b b a Figure 10: Possible interleavings. Figure 11: A precubical set representing three concurrent accesses to a semaphore initialized to 2. The usual way to define a precubical set is to define the boundary operators; for ....

Pratt, V., Chu spaces: Automata with quantum aspects, Technical report, Stanford University (1994).

....of measurements is explained by quantum logic in section 4. The quantum computations are done reversible so they can be implemented deterministic. In section 5 the notions for the mathematical semantic of the reversible computations is explained. The treatment is grounded on Vaughan Pratt s work [Pra93, Pra94a] as a strong interconnection of Chu spaces, linear logic and concurrency. This leads to a proposal for a Chu space which models the behavior of quantum computation. 2 Type Theory To go a step further in reliability of software one approach is to treat programming languages formal. This should ....

Vaughan Pratt. Chu spaces: Automata with quantum aspects. In Proc. Workshop on Physics and Computation, pages 186--195, Dallas, 1994. IEEE.

....by Pratt and his collaborators as a foundational structure for concurrency theory, capturing the duality of states and y This work was partly supported under CEC grant ERBCHBGCT930496 and under ONR grant N00014 92 J 1974. D. Pavlovi c 2 events (Gupta and Pratt 1993; Pratt 1993a; Pratt 1993b; Pratt 1994a; Pratt 1994b; Gupta 1994; Glabbeek and Plotkin 1995; Pratt 1995) They were shown to be remarkably rich and versatile, accomodating concrete faithful functors from arbitrary small concrete categories. However, no categorical universal property (Mac Lane 1971, ch. III) of the Chu construction has ....

....his collaborators as a foundational structure for concurrency theory, capturing the duality of states and y This work was partly supported under CEC grant ERBCHBGCT930496 and under ONR grant N00014 92 J 1974. D. Pavlovi c 2 events (Gupta and Pratt 1993; Pratt 1993a; Pratt 1993b; Pratt 1994a; Pratt 1994b; Gupta 1994; Glabbeek and Plotkin 1995; Pratt 1995) They were shown to be remarkably rich and versatile, accomodating concrete faithful functors from arbitrary small concrete categories. However, no categorical universal property (Mac Lane 1971, ch. III) of the Chu construction has been ....

Pratt, V.R. (1994) Chu Spaces: Automata with quantum aspects, In Proc. Workshop on Physics and Computation. IEEE Computer Society Press.

....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. R. Pratt, "Chu Spaces: Automata with Quantum Aspects", In: Proceedings Workshop on Physics and Computation (PhysComp'94), Dallas, IEEE, 1994, pp. 186--195.

....(5) Going to transition systems is precisely a step towards identifying (more tractable ) classes of properties we are interested in. Going to (prime, stable etc. event systems [Win88] or to pomsets, event spaces [Pra86, Pra91a] is the main other strand, Petri nets [BRG87] and Chu spaces [Pra94] being somewhat in between. But there is also a balance in the structuring process of sets (like the transition relation between states, or like the partial orders between events etc. we find in these models. These should be well designed so that points (1) 2) 3) and (4) receive satisfactory ....

V. Pratt. Chu spaces: Automata with quantum aspects. Technical report, Stanford University, 1994.

.... regard to utility, besides the motivating application to concurrent computation, Chu spaces find application in mathematics, where they organize relational structures, topology, and duality into a unified framework [Pra95b] physics, where they provide a process interpretation of wavefunctions [Pra94a]; and philosophy, where they offer a solution to Descartes problem of the mechanism by which the mind interacts with the body [Pra95a] Common to these applications is the construction of everything in the domain in question in terms of the interaction of appropriate polar opposites in the ....

V.R. Pratt. Chu spaces: Automata with quantum aspects. In Proc. Workshop on Physics and Computation (PhysComp'94), Dallas, 1994. IEEE.

....Hilbert space. Furthermore the progression from automata to Chu spaces recapitulates the progression from Langrangian mechanics retaining even some of the essential properties of the Legendre transform by which this passage is standardly accomplished. Some of these connections are developed in [Pra93a, Pra94b], although the details of this second point of contact have only become clear to us since then. These connections get considerably closer to the essence of quantum mechanics than does quantum logic [BvN36] which abstracts away from complementarity to capture just the underlying projective ....

V.R. Pratt. Chu spaces: Automata with quantum aspects. In Proc. Workshop on Physics and Computation (PhysComp'94), Dallas, 1994. IEEE.

....problems of causal interaction in physics. 1 Cartesian Dualism The Chu construction [Bar79] strikes us as extraordinarily useful, more so with every passing month. Elsewhere we have described the application of Chu spaces to process algebra [GP93] metamathematics [Pra93, Pra94a] and physics [Pra94b]. Here we make a first attempt at applying them to philosophy. It might seem that traditional philosophical questions would be beyond the scope of TAPSOFT. Bear in mind however that Boolean logic as the basis for computer circuits was born of philosophy (and a little statistics) Only slightly ....

V.R. Pratt. Chu spaces: Automata with quantum aspects. In Proc. Workshop on Physics and Computation (PhysComp'94), Dallas, 1994. IEEE.

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