On the Computational Complexity of Conservative Computing

  title={On the Computational Complexity of Conservative Computing},
  author={Giancarlo Mauri and Alberto Leporati},
In a seminal paper published in 1982, Fredkin and Toffoli have introduced conservative logic, a mathematical model that allows one to describe computations which reflect some properties of microdynamical laws of Physics, such as reversibility and conservation of the internal energy of the physical system used to perform the computations. In particular, conservativeness is defined as a mathematical property whose goal is to model the conservation of the energy associated to the data which are… 
Simulating the Fredkin Gate with Energy-Based P Systems
This paper introduces energy–based P systems as a parallel and distributed model of computation in which the amount of energy manipulated and/or consumed during computations is taken into account and shows how energy– based P systems can be used to simulate the Fredkin gate.
Conservative Computations in Energy-Based P Systems
It is shown that conservative computations performed by energy–based P systems naturally allow to define an NP–hard optimization problem, here referred to as Min Storage, and a corresponding NP–complete decision problem, ConsComp.


Towards a Theory of Conservative Computing
We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation
Conservative logic
Conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation and proves that universal computing capabilities are compatible with the reversibility and conservation constraints.
Fredkin gates for finite-valued reversible and conservative logics
The basic principles and results of conservative logic introduced by Fredkin and Toffoli in 1982, on the basis of a seminal paper of Landauer, are extended to d-valued logics, with a special
Irreversibility and heat generation in the computing process
Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.
Logical reversibility of computation
This result makes plausible the existence of thermodynamically reversible computers which could perform useful computations at useful speed while dissipating considerably less than kT of energy per logical step.
ON ACC and threshold circuits
  • A. Yao
  • Computer Science
    Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science
  • 1990
It is proved that any language in ACC can be approximately computed by two-level circuits of size 2 raised to the (log n)/sup k/ power, with a symmetric-function gate at the top and only AND gates on the first level, giving the first nontrivial upper bound on the computing power of ACC circuits.
Computers and Intractability: A Guide to the Theory of NP-Completeness
Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge
On ACC (circuit complexity)
  • R. Beigel, J. Tarui
  • Computer Science
    [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
  • 1991
The authors simplify Yao's proof and strengthen his results: every language in ACC is recognized by a sequence of depth-2 deterministic circuits with a symmetric gate at the root and n/sup polylog/(n) AND gates of fan-in polylog(n) at the leaves.
It is shown that every languageL in the class ACC can be recognized by depth-two deterministic circuits with a symmetric-function gate at the root and polynomialspn overZ of degree logO(1)n and with coefficients of magnitude.