Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes

Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes

Upward Separation for FewP and Related Classes

This paper studies the range of application of the upward separation technique that has been introduced by Hartmanis to relate certain structural properties of polynomial-time complexity classes to their exponential-time analogs and was rst applied to NP [Har83]. Later work revealed the limitations of the technique and identi ed classes defying upward separation. In particular, it is known that...

Reversible Simulation of Irreversible Computation

Computer computations are generally irreversible while the laws of physics are reversible. This mismatch is penalized by among other things generating excess thermic entropy in the computation. Computing performance has improved to the extent that eeciency degrades unless all algorithms are executed reversibly, for example by a universal reversible simulation of irreversible computations. All k...

Complexity Classes Deened by Counting Quantiiers*

We study the polynomial time counting hierarchy, a hierarchy of complexity classes related to the notion of counting. We investigate some of their structural properties, settling many open questions dealing with oracle characterizations, closure under boolean operations, and relations with other complexity classes. We develop a new combinatorial technique to obtain relativized separations for s...

Some Results on Relativized Deterministic and Nondeterministic Time Hierarchies

Relativized forms of deterministic and nondeterministic time complexity classes are considered. It is shown, at variance with recently published observations, that one basic step by step simulation technique in complexity theory does not relativize (i.e., does not generalize to computations with oracles), using the current definitions for time and space complexity of oracle computations. A new ...