Speedup for Natural Problems
نویسندگان
چکیده
Informally, a language L has speedup if, for any Turing machine (TM) for L, there exists one that is better. Blum [1] showed that there are computable languages that have almost-everywhere speedup. These languages were unnatural in that they were constructed for the sole purpose of having such speedup. We identify an intuitive condition which, like several others in the literature, implies that accepting any coNP -complete language has an infinitely-often (i.o.) superpolynomial speedup. We also exhibit a natural problem which unconditionally has a weaker type of i.o. speedup based upon whether the full input is read. Neither speedup pertains to the worst case.
منابع مشابه
An approach to Improve Particle Swarm Optimization Algorithm Using CUDA
The time consumption in solving computationally heavy problems has always been a concern for computer programmers. Due to simplicity of its implementation, the PSO (Particle Swarm Optimization) is a suitable meta-heuristic algorithm for solving computationally heavy problems. However, despite the simplicity, the algorithm is inefficient for solving real computationally heavy problems but the pr...
متن کاملA generalized implicit enumeration algorithm for a class of integer nonlinear programming problems
Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...
متن کاملSpeedup for Natural Problems and NP=?coNP
Informally, a language L has speedup if, for any Turing machine (TM) for L, there exists one that is better. Blum [2] showed that there are computable languages that have almost-everywhere speedup. These languages were unnatural in that they were constructed for the sole purpose of having such speedup. We identify a condition apparently only slightly stronger than P 6= NP which implies that acc...
متن کاملSpeedup for natural problems and noncomputability
A resource-bounded version of the statement “no algorithm recognizes all non-halting Turing machines” is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any (paddable) coNPcomplete language and also equivalent to a superpolynomial speedup in proof length in propositional proof systems for tautologies, each of which implies P 6= NP. This suggests ...
متن کاملStrict Sequential P-completeness
In this paper we present a new notion of what it means for a problem in P to be inherently sequential. Informally, a problem L is strictly sequential P-complete if when the best known sequential algorithm for L has polynomial speedup by parallelization, this implies that all problems in P have a polynomial speedup in the parallel setting. The motivation for defining this class of problems is to...
متن کامل