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We prove that the families matrix powering, iterated matrix product, and adjoint matrix are VQP-complete, where VQP denotes Valiant’s class of quasipolynomial-computable families of multivariate polynomials. This proves a conjecture by Bürgisser [3, Conjecture 8.1].
The paper presents a simple construction ofp olynomial length universal traversal sequences for cycles. These universal traversal sequences are log-space (even NC1) constructible and are oflength O(n4.03). Our result improves the previously known upper-bound O(n4.76) for logspace constructible universal traversal sequences for cycles.
A language is universally polynomial if its intersection with every NP-complete language is in P. Such a language would provide an automatic method for generating easy instances of intractable problems. In this note, we give a complete characterization of universally polynomial languages that are context-free, answering an open question in [4].
This paper gives an exponential separation on the depth of branching programs (BPs) between oblivious and non-oblivious BPs. Namely, there is a difference just like the difference between sequential and NC computation: (i) There is a Boolean function f1 of N variables which can be computed by a polynomial-size, syntactic BP with a depth of 2 logN - log logN + 1 but cannot be computed by any oblivious...
We prove that a very basic class of program schemes augmented with access to a queue and an additional numeric universe within which counting is permitted accepts exactly the class of recursively solvable problems. The class of problems accepted when access to the numeric universe is removed is exactly the class of recursively solvable problems that are closed under extensions. We build upon NSPQ(1)...
Karp and Lipton, in their seminal 1980 paper, introduced the notion of advice (nonuniform) complexity, which since has been of central importance in complexity theory. Nonetheless, much remains unknown about the optimal advice complexity of classes having polynomial advice complexity. In particular, let P-sel denote the class of all P-selective sets [23] For the nondeterministic advice complexity...
P-complete problems seem to have no parallel algorithm which runs in polylogarithmic time using a polynomial number of processors. A P-complete problem is in class EP (Efficient and Polynomially fast) if and only if there exists a cost optimal algorithm to solve it in T(n) = O(t(n)€) (€ lt; 1) using P(n) processors such that T(n)×P(n) = O(t(n)), where t(n) is the time complexity of the fastest...
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