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 manipulated during the computation of a logic gate. Extending such notion to generic gates whose input and output lines may assume a finite number d of truth values, we define conservative computations and we show that they naturally induce a new NP–complete decision problem and an associated NP–hard optimization problem. Moreover, we briefly describe the results of five computer experiments performed to study the behavior of some polynomial time heuristics which give approximate solutions to such optimization problem. Since the computational primitive underlying conservative logic is the Fredkin gate, we advocate the study of the computational power of Fredkin circuits, that is circuits composed by Fredkin gates. Accordingly, we give some first basic results about the classes of Boolean functions which can be computed through polynomial–size constant–depth Fredkin circuits.
Mauri, G., & Leporati, A. (2003). On the computational complexity of conservative computing. In Proc. MFCS 2003 – Mathematical Foundations of Computer Science (pp.92-112). Berlin : Springer [10.1007/978-3-540-45138-9_5].
|Citazione:||Mauri, G., & Leporati, A. (2003). On the computational complexity of conservative computing. In Proc. MFCS 2003 – Mathematical Foundations of Computer Science (pp.92-112). Berlin : Springer [10.1007/978-3-540-45138-9_5].|
|Tipo:||slide + paper|
|Carattere della pubblicazione:||Scientifica|
|Presenza di un coautore afferente ad Istituzioni straniere:||No|
|Titolo:||On the computational complexity of conservative computing|
|Autori:||Mauri, G; Leporati, A|
|Data di pubblicazione:||2003|
|Nome del convegno:||Mathematical Foundations of Computer Science|
|Serie:||LECTURE NOTES IN COMPUTER SCIENCE|
|Appare nelle tipologie:||02 - Intervento a convegno|