Title :
DSPACE [nk]=VAR[k+1]
Author_Institution :
Dept. of Comput. & Inf. Sci., Massachusetts Univ., Amherst, MA, USA
fDate :
30 Jun-3 Jul 1991
Abstract :
The author proves that the set of properties checkable by a Turing machine in DSPACE[nk] is exactly equal to the set of properties describable by a uniform sequence of first-order sentences using at most k+1 distinct variables. He proves that this is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE=VAR[O[1]]. The author suggests some directions for exploiting this result to derive tradeoffs between the number of variables and the quantifier-depth in descriptive complexity. This has applications to parallel complexity
Keywords :
Turing machines; computational complexity; Turing machine; descriptive complexity; distinct variables; first-order sentences; iterative definition; parallel complexity; quantifier-depth; relations; uniform sequence; Logic circuits; Polynomials; Vocabulary;
Conference_Titel :
Structure in Complexity Theory Conference, 1991., Proceedings of the Sixth Annual
Conference_Location :
Chicago, IL
Print_ISBN :
0-8186-2255-5
DOI :
10.1109/SCT.1991.160278
