Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
The Complexity of Problems Concerning Graphs with Regularities (Extended Abstract)
Proceedings of the Mathematical Foundations of Computer Science 1984
The Complexity of Membership Problems for Circuits over Sets of Natural Numbers
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Hi-index | 0.00 |
A finite recurrent system over the power set of the natural numbers of dimension n is a pair composed of nn-ary functions over the power set of the natural numbers and an n-tuple of singleton sets of naturals. Every function is applied to the components of the tuple and computes a set of natural numbers, that might also be empty. The results are composed into another tuple, and the process is restarted. Thus, a finite recurrent system generates an infinite sequence of n-tuples of sets of natural numbers. The last component of a generated n-tuple is the output of one step, and the union of all outputs is the set defined by the system. We will consider only special finite recurrent systems: functions are built from the set operations union (∪), intersection (∩) and complementation (–) and the arithmetic operations addition (⊕) and multiplication (⊗). Sum and product of two sets of natural numbers are defined elementwise. We will study two types of membership problems: given a finite recurrent system and a natural number, does the set defined by the system contain the queried number, and does the output of a specified step contain the queried number? We will determine upper and lower bounds for such problems where we restrict the allowed operations to subsets of {∩,∪,−−,⊕,⊗}. We will show completeness results for the complexity classes NL, NP and PSPACE.