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In this paper we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that given an arithmetic circuit (either explicitly or via black-box access) that computes a multivariate polynomial f, the task of computing arithmetic circuits for the factors of f can be solved deterministically,...
We propose a built-in scheme for generating all patterns of a given deterministic test set T. The scheme is based on grouping the columns of T, so that in each group of columns the number ri of unique representatives (row subvectors) as well as their product R over all such groups is kept at a minimum. The representatives of each group (segment) are then generated by a small finite state machine (FSM)...
This document presents a compilation of results from tests performed by iRoC Technologies on SER induced by alpha particles on SRAM memories for technology nodes from 180 nm to 65 nm. The aim of this study is to establish the variation of sensitivity with technology node for SEU and MCU, and to analyze the possible influence of different designs and technological parameters at a given technology node.
In this paper, we present a systematic method for the designing fault tolerant reversible arithmetic circuits for finite field or Galois fields of the form GF(2m). To tackle the problem of errors in computation, we propose error detection and correction using multiple parity prediction technique based on low density parity check (LDPC) code. For error detection and correction, we need additional garbage...
Measurement of visual quality is of fundamental importance to many image and video processing applications. Traditionally, quality assessment metrics predict visual quality following the paradigm of modeling the known properties of the Human Visual System (HVS). The Structural Similarity (SSIM) index is a new approach which assumes that the HVS is highly adapted for extracting structural information...
It is shown that the problem of deciding and constructing a perfect matching in bipartite graphs G with the polynomial permanents of their n × n adjacency matrices A (perm(A) = nO(1)) are in the deterministic classes NC2 and NC3, respectively. We further design an NC3 algorithm for the problem of constructing all perfect matchings (enumeration problem) in a graph G with a permanent bounded by O(nk)...
Random Polynomial Time (Rp) is currently considered to be the class of tractable computational problems. Here one assumes a source of truly random bits. However, the known sources of randomness are imperfect. They can be modeled as an adversary source, called slightly-random source. Slightlyrandom Polynomial Time (SRp) is the class of problems solvable in polynomial time using such a source. SRp is...
We show that the permutation group membership problem can be solved in depth (logn)3 on a Monte Carlo Boolean circuit of polynomial size in the restricted case in which the group is abelian. We also show that this restricted problem is NC1-hard for NSPACE(logn).
A complexity theory for unbounded fan-in parallelism is developed where the complexity measure is the simultaneous measure (number of processors, parallel time). Two models of unbounded fan-in parallelism are (1) parallel random access machines that allow simultaneous reading from or writing to the same common memory location, and (2) circuits containing AND's, OR's and NOT's with no bound placed...
Straight line programs in which array elements can be referenced and set are considered. Two programs are equivalent if they compute the same expression as a function of the inputs. Testing the equivalence of programs with arrays is shown to be NP-complete, while programs without arrays can be tested for equivalence in linear time. Equivalence testing takes polynomial time when programs have either...
Decision procedures for validity in intuitionistic propositional calculus and modal propositional calculus are given which require a running time proportional to a polynomial in the length of the formula on a nondeterministic Turing machine. Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic...
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