For a time-constructible function T we give an explicit language L T which can be recognized in time T (n). We prove that any Turing machine that recognizes L T requires time close to T (n) for most inputs, thus forming an average time hierarchy. The existence of the average time hierarchy

Motivated by results on interactive proof systems we investigate an 9-8-hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomial-time hierarchy, is called the analytic polynomial-time hierarchy. It is shown

, the framework is used to help explain how electronic markets and electronic hierarchies will allow closer integration of adjacent steps in the value added chains of our economy. The most surprising prediction is that information technology will lead to an overall shift toward proportionately more coordination

Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory

We study the existence of time hierarchies for heuristic algorithms. We prove that a time hierarchy exists for heuristics algorithms in such syntactic classes as NP and coNP, and also in semantic classes AM and MA. Earlier, Fortnow and Santhanam (FOCS’04) proved the existence of a time hierarchy

Abstract. In this paper, two interesting complexity classes, PP and P, are compared with PH, the polynomial-time hierarchy. It is shown that every set in PH is polynomial-time Turing reducible to a set in PP, and PH is included in BP. 0)P. As a consequence of the results, it follows thatPPPH (or 03

of variables in the formula, we have been unable to prove super-linear time lower bounds on random access machinesdespite several decades of effort. Additionally, problems complete for higher levels of the polynomial-time hierarchy, while not receiving as much attention, havealso resisted nontrivial time lower

This memo describes the Network Time Protocol (NTP) designed to distribute time information in a large, diverse internet system operating at speeds from mundane to lightwave. It uses a returnabletime architecture in which a distributed subnet of time servers operating in a self

The bounded arithmetic theory S 2 is finitely axiomatized if and only if the polynomial hierarchy provably collapses. If T 2 equals S then T 2 is equal to S 2 and proves that the polynomial time hierarchy collapses to # , and, in fact, to the Boolean hierarchy over # and to # i+1

Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis