Measuring in PSPACE
نویسنده
چکیده
Results of the kind \Almost every oracle in exponential space separates P from NP" or \Almost every set in exponential time is P-bi-immune" can be precisely formulated via a new approach in Structural Complexity recently introduced by Lutz. He deenes a resource-bounded measure in exponential time and space classes that generalizes Lebesgue measure, a powerful mathematical tool. We investigate here the possibility of extending this resource-bounded measure to other classes, mainly PSPACE. We prove here that the natural candidate of a resource bound for measuring in PSPACE is not valid unless some unlikely consequences are true. We then obtain a weaker way of measuring in PSPACE that lacks a property that resource-bounded measure has in bigger classes.
منابع مشابه
Measuring 4-local qubit observables could probabilistically solve PSPACE
We consider a hypothetical apparatus that implements measurements for arbitrary 4-local quantum observables A on n qubits. The apparatus implements the “measurement algorithm” after receiving a classical description of A. We show that a few precise measurements, applied to a basis state would provide a probabilistic solution of PSPACE problems. The error probability decreases exponentially with...
متن کاملReliable Reductions High Sets and Low Sets
Measuring the information content of a set by the space bounded Kolmogorov complexity of its characteristic sequence we investigate the non uniform com plexity of sets A in EXPSPACE poly that reduce to some set having very high information content Speci cally we show that if the reducibility used has a certain property called reliability then A in fact is reducible to a sparse set under the sam...
متن کاملParametric Temporal
We extend the standard model checking paradigm of linear temporal logic, LTL, to a \model measuring" paradigm where one can obtain more quantitative information beyond a \Yes/No" answer. For this purpose, we deene a parametric temporal logic, PLTL, which allows statements such as \a request p is followed in at most x steps by a response q," where x is a free variable. We show how one can, given...
متن کاملIs P = PSPACE for Infinite Time Turing Machines?
question P ? = NP for Infinite Time Turing Machines, and several variants on it, are treated in e.g. [Sc], [DeHaSc], and [HaWe]. Besides time complexity, we may also try to look at issues of space complexity in ITTMs. However, because an ITTM contains tapes of length ω, and all nontrivial ITTM computations will use the entire, ω-length tape, simply measuring the space complexity by counting the...
متن کاملNotes on Complexity Theory Last updated : October , 2015 Lecture 6
As in our previous study of NP, it is useful to identify those problems that capture the essence of PSPACE in that they are the “hardest” problems in that class. We can define a notion of PSPACE-completeness in a manner exactly analogous to NP-completeness: Definition 1 Language L′ is PSPACE-hard if for every L ∈ PSPACE it holds that L ≤p L′. Language L′ is PSPACE-complete if L′ ∈ PSPACE and L′...
متن کامل