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A new two-person pebble game that models parallel computations is defined. This game extends the two-person pebble game defined in [DT85] and is used to characterize two natural parallel complexity classes, namely LOGCFL and AG1. The characterizations show a fundamental way in which the computations in these two classes differ. This game model also unifies the proofs of some well known results of...
An m-degree is a collection of sets equivalent under polynomial-time many-one (Karp) reductions; for example, the complete sets for NP or PSPACE are m-degrees. An m-degree is collapsing iff its members are p-isomorphic, i.e., equivalent under polynomial time, 1-1, onto, polynomial time invertible reductions. L. Berman and J. Hartmanis showed that all the then known natural NP-complete sets are isomorphic,...
We give an algorithm to construct a cell decomposition of Rd, including adjacency information, defined by any given set of rational polynomials in d variables. The algorithm runs in single exponential parallel time, and in NC for fixed d. The algorithm extends a recent algorithm of Ben-Or, Kozen, and Reif for deciding the theory of real closed fields.
This paper investigates the computational complexity of planning the motion of a body B in 2-D or 3-D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence that the 3-D dynamic movement problem is...
The complexity of priority queue operations is analyzed with respect to the cell probe computational model of A. Yao. A method utilizing families of hash functions is developed which permits priority queue operations to be implemented in constant worst case time provided that a size constraint is satisfied. The minimum necessary size of a family of hash functions for computing the rank function is...
We study probabilistic on-line simulators for several machine models (or memory structures). The simulators have a more constrained access to data than the virtual machines, but are allowed to use probabilistic means to improve average access time. We show that in many cases coin tosses can not make up for inadequate access.
In this paper we define a generalized, two-parameter, Kolmogorov complexity of finite strings which measures how much and how fast a string can be compressed and we show that this string complexity measure is an efficient tool for the study of computational complexity. The advantage of this approach is that it not only classifies strings as random or not random, but measures the amount of randomness...
A language L is random with respect to a given complexity class C if for all ′ ∈ C L and ′ disagree on half of all strings. It is known that for any complexity class there are recursive languages that are random with respect to that class. Here it is shown that there are tight space and time hierarchies of random languages, and that EXPTIME contains P-isomorphism classes containing only languages...
This paper describes circuits for computation of various algebraic functions on polynomials, power series, integers, and reals for which it has been a long standing open problem to compute in depth less then (log n)2. Let R[x] be the polynomials and power series over a commutative ring which supports a fast Fourier transform and let L[x] be the polynomials and power series over the rationals L. For...
The Diffie and Hellman model of a Public Key Cryptosystem has received much attention as a way to provide secure network communication. In this paper, we show that the original Diffie and Hellman model does not guarantee security against other users in the system. It is shown how users, which are more powerful adversarys than the traditionally considered passive eavesdroppers, can decrypt other users...
We introduce a property of boolean functions, called transitivity which holds of integer, polynomial, and matrix products as well as of many interesting related computational problems. We show that the area of any circuit computing a transitive function grows quadratically with the circuit's maximum data-rate, expressed in bit/second. This result provides a precise analytic expression of an area-time...
We study the power of RAM acceptors with several instruction sets. We exhibit several instances where the availability of the division operator increases the power of the acceptors. We also show that in certain situations parallelism and stochastic features ('distributed random choices') are provably more powerful than either parallelism or randomness alone. We relate the class of probabilistic Turing...
We consider uniform circuit complexity, introduced by Borodin as a model of parallel complexity. Three main results are presented. First, we show that simultaneous size/depth of uniform circuits is the same as space/time of alternating Turing machines, with depth and time within a constant factor and likewise log(size) and space. Second, we apply this to characterize the class of polynomial size and...
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