### Nonconstructive tools for proving polynomial-time decidabilityNonconstructive tools for proving polynomial-time decidability

Access Restriction
Subscribed

 Author Fellows, Michael R. ♦ Langston, Michael A. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1988 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Recent advances in graph theory and graph algorithms dramatically alter the traditional view of concrete complexity theory, in which a decision problem is generally shown to be in P by producing an efficient algorithm to solve an optimization version of the problem. Nonconstructive tools are now available for classifying problems as decidable in polynomial time by guaranteeing only the $\textit{existence}$ of polynomial-time $\textit{decision}$ algorithms. In this paper these new methods are employed to prove membership in P for a number of problems whose complexities are not otherwise known. Powerful consequences of these techniques are pointed out and their utility is illustrated. A type of partially ordered set that supports this general approach is defined and explored. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1988-06-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 35 Issue Number 3 Page Count 13 Starting Page 727 Ending Page 739

#### Open content in new tab

Source: ACM Digital Library