Grundsätzliches zur Beschreibung Diskreter Prozesse

Petri, C. A.

doi:10.1007/978-3-0348-5879-3_10

Cited by 38 publications

(11 citation statements)

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“…the germinal ideas of Petri's (1967). For conservative logic, we acknowledge contributions by E. Barton and D. Silver; and for the billiard ball model contributions by R. Feynman, N. Margolus, and A. Ressler.…”

Section: Acknowledgmentsmentioning

confidence: 98%

Conservative logic

Fredkin¹,

Toffoli²

1982

Int J Theor Phys

1,850

801

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Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certain additit, e quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of high-performance computing systems, i.e., of systems that make very efficient use of the "computing resources" actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary, variables and is the conservative-logic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical "balls," and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a general-purpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions.

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Section: Acknowledgmentsmentioning

confidence: 98%

Conservative logic

Fredkin¹,

Toffoli²

1982

Int J Theor Phys

1,850

801

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“…The gate T (n,m,1) is very similar to a gate introduced by Petri in Petri (1967). For n = m = 1, we obtain the well known Toffoli gate (Toffoli, 1980), which is essentially identical to Feynman's Controlled-Controlled-NOT gate.…”

Section: Definition 22 (Thementioning

confidence: 96%

Qubit Semantics and Quantum Trees

et al. 2005

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In the qubit semantics the meaning of any sentence α is represented by a quregister: a unit vector of the n-fold tensor product ⊗ n C 2 , where n depends on the number of occurrences of atomic sentences in α (see Cattaneo et al.). The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence α gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of α can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of α into the quregister associated to α.KEY WORDS: quantum computation; quantum logic.

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“…We will consider the following gates: the negation, the square root of the negation, the square root of the identity and the Petri-Toffoli gate (Petri, 1967).…”

Section: Fock Quantum Computational Structuresmentioning

confidence: 99%

Quantum Computational Semantics on Fock Space

et al. 2005

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In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space F based on the Hilbert space C 2 . Generally, the meaning of a sentence is smeared over different sectors of F . The standard quantum computational semantics is a limit case of the Fock space semantics, where the meaning of any sentence α only "lives" in one sector of F , which is determined by the logical complexity of α. We prove that the global Fock space semantics and the standard quantum computational semantics characterize the same logic.

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Grundsätzliches zur Beschreibung Diskreter Prozesse

Cited by 38 publications

References 0 publications

Conservative logic

Conservative logic

Qubit Semantics and Quantum Trees

Quantum Computational Semantics on Fock Space

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