Abstract:
We study the relationship between probabilistic and unambiguous computation, and provide strong relativized evidence that they are incomparable. In particular, we display a relativized world in which the complexity classes embodying these paradigms of computation are mutually immune. We answer questions formulated in---and extend the line of research opened by---Geske and Grollman [15] and Balcazar and Russo [3]. 1 Introduction: Why Compare Computational Paradigms? Many complexity classes have been defined in recent years to characterize the computational powers of natural approaches to computation. However, # Some of these results were announced at the 1989 International Conference on Computing and Information, Toronto, Canada. + Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA 94304. Research performed in part while at Columbia University, supported in part by NSF grants DCR-85-11713 and CCR-86-05353. # Department of Computer Science, University of Roc...
Citations
|
2870
|
Introduction to automata theory, languages and computation
– Hopcroft, Ullman
- 1979
|
|
575
|
Theory of Recursive Functions and Effective Computability
– Rogers
- 1967
|
|
200
|
Computational complexity of probabilistic turing machines
– Gill
- 1975
|
|
129
|
Complexity Measures for Public-Key Cryptosystems
– Grollmann, Selman
- 1988
|
|
127
|
A complexity theoretic approach to randomness
– Sipser
- 1983
|
|
76
|
Generic oracles and oracle classes
– Blum, Impagliazzo
- 1987
|
|
74
|
Relative complexity of checking and evaluation
– Valiant
- 1976
|
|
71
|
The boolean hierarchy I: Structural properties
– Cai, Gundermann, et al.
- 1988
|
|
66
|
BPP and the Polynomial Hierarchy
– Lautemann
- 1983
|
|
49
|
On the power of parity polynomial time
– Cai, Hemachandra
- 1990
|
|
46
|
The strong exponential hierarchy collapses
– Hemachandra
- 1989
|
|
45
|
Complexity classes without machines: on complete languages for UP
– Hartmanis, Hemachandra
- 1988
|
|
44
|
On the unique satisfiability problem
– Gurevich
- 1982
|
|
43
|
Relativizations of the P=?NP question
– Baker, Gill, et al.
- 1975
|
|
38
|
The boolean hierarchy II: Applications
– Cai, Gundermann, et al.
- 1989
|
|
36
|
The isomorphism conjecture fails relative to a random oracle
– Kurtz, mahaney, et al.
- 1989
|
|
28
|
Limits on the Provable Consequences of One-Way Functions
– Rudich
- 1988
|
|
18
|
Relativized questions involving probabilistic algorithms
– Rackoff
- 1982
|
|
14
|
Probabilistic quantifiers, adversaries, and complexity classes: an overview
– Zachos
- 1986
|
|
13
|
On the relativized power of additional accepting paths
– Beigel
- 1989
|
|
9
|
Relativizations of unambiguous and random polynomial time classes
– Geske, Grollmann
- 1986
|
|
9
|
Solvable problems with conflicting relativizations
– Hartmanis
- 1985
|
|
5
|
On the power of probabilistic polynomial time: P NP[log] ` PP
– Hemachandra, Wechsung
- 1989
|
|
5
|
Counting classes with finite acceptance types
– Gundermann, Wechsung
- 1987
|
|
4
|
Immunity and simplicity in relativizations of probabilistic complexity classes
– Balcázar, Russo
- 1988
|
|
3
|
Oracles for deterministic versus alternating classes
– Gasarch
- 1987
|
|
3
|
On probabilistic computations with restricted access to NP oracles, manuscript
– Toda
- 1988
|
|
2
|
Relativizations comparing NP and exponential time
– Gasarch, Homer
- 1983
|
|
2
|
Structure of complexity classes: Separations, collapses, and completeness
– Hemachandra
- 1988
|
|
2
|
Immunity, relativization, and nondeterminism
– Schöning, Book
- 1984
|
|
1
|
Relative to a random oracle A,P A �=NP A with probability 1
– Bennett, Gill
- 1981
|
|
1
|
Upward translation and immunity
– Eppstein, Hemachandra
|
|
1
|
Oracle constructions to prove all possible relationships between relativizations of P
– Lischke
- 1986
|
