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We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather, the distribution is inherent to the cylindrical structure and determined mostly by the number of variables. This insight is then combined with an algorithm that...
In this paper, the intractable problem of finding the prime factors of an integer has been represented as the integer programming problem to be solved using nature inspired heuristics. Integer factorization is a one-way mathematical function and because of its computational intractability, it is frequently used in public key cryptography, for example in RSA encryption systems. Since integer factorization...
Artifact consists of information model and lifecycle. Artifact lifecycle defined by the business departments according to business rules and other relative constraints are used for business's compliance checks and process's real-time monitoring, so how to construct artifact lifecycle model is crucial, it can be used to judge the violations in the business process. In this paper, we adopt FSM (Finite-State-Machine)...
The research presented focuses on implementation of RF digital predistorters using polynomial optimization techniques. By representing the system with a set of two polynomials, we have been able to apply algebraic techniques resulting in reduction in cost of implementing digital predistorters. To test this approach we have used model of a communication channel using traveling wave tube amplifier and...
Finding the list of all minimal solutions of a fuzzy relational system is a tough work. Actually it has been proved to be NP hard recently by Markovskii. (A.V. Markovskii, On the relation between equations with max-product composition and the covering problem. Fuzzy Sets Systems 153, pp. 261–273, 2005). However, practical programs for solving these problems usually run much faster than they are supposed...
Fixed parameter approach is one of the theoretically rich and useful design technique to deal with NP-completeness. It analizes running times both in terms of input size and the parameter. The fixed parameter O(1) tractable problems can be solved in time f (k)∗nO(1)(where n is the size of the given object) for some computable function f. Three design techniques: depth-bounded search trees, kernelization,...
In this paper, we investigate the verification issue for safe diagnosability of fuzzy discrete-event systems (FDESs). In order to guarantee that faults occurring in a safe diagnosable fuzzy system can be detected with a certain degree, and the detection may be completed before any unsafe behavior is executed, we construct a nondeterministic automaton, namely verifier, to check whether a certain forbidden...
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,...
The title of this paper is meant to highlight an emerging duality between two fundamental topics in algorithms and complexity theory. Algorithms for circuits} refers to the design of interesting algorithms which can perform non-trivial circuit analysis of some kind, on either a circuit or a Boolean function given as a truth table. For instance, an algorithm determining whether a given circuit has...
This paper summarizes work that investigates human interactions in terms of communication through motion in cooperative control. We are interested in multi-agent distributed control models with a shared goal and with the agents being required to accomplish secondary objectives. The study presented here extends the earlier work on the analysis of leader-follower interactions in salsa. The move transitions...
We give a length-efficient puncturing of Reed-Muller codes which preserves its distance properties. Formally, for the Reed-Muller code encoding n-variate degree-d polynomials over F_q with q gtrsim d/delta, we present an explicit (multi)-set S subseteq F_q^n of size N=mathrm {poly}(n^d/delta) such that every nonzero polynomial vanishes on at most delta N points in S. Equivalently, we give an explicit...
In recent years there has been much exciting progress on depth reduction of arithmetic circuits and lower bounds for bounded depth arithmetic circuits. We will survey some of these results and highlight some of the main challenges and open questions that remain.
A c-short program for a string x is a description of x of length at most C(x) + c, where C(x) is the Kolmogorov complexity of x. We show that there exists a randomized algorithm that constructs a list of n elements that contains a O(log n)-short program for x. We also show a polynomial-time randomized construction that achieves the same list size for O(log^2 n)-short programs. These results beat the...
The isomorphism problem for groups given by their multiplication tables (GPI) has long been known to be solvable in n^O(log n) time, but only recently has there been significant progress towards polynomial time. For example, Babai et al. (ICALP 2012) gave a polynomial-time algorithm for groups with no abelian normal subgroups. Thus, at present it is crucial to understand groups with abelian normal...
We give new characterizations and lower bounds relating classes in the communication complexity polynomial hierarchy and circuit complexity to limited memory communication models. We introduce the notion of rectangle overlay complexity of a function f. This is a natural combinatorial complexity measure in terms of combinatorial rectangles in the communication matrix of f. Furthermore, we consider...
We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size nW(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(w) is essentially tight. Moreover, our lower bounds can be generalized to polynomial calculus resolution (PCR) and Sherali-Adams, implying that...
We show that most algebraic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique (Nisan-Wigderson), the results of Razborov and Smolensky on AC^0[p], multilinear formula and circuit size lower bounds (Raz et al.), the degree bound (Strassen, Baur-Strassen),...
We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from Arthur. One motivation for this model (which we explore in detail) comes from the close analogies between it and the quantum complexity class QMA(k), but the AM(k)...
For a function f over the discrete cube, the total L1 influence of f is defined as the sum of the L1 norm of the discrete derivatives of f in all n directions. In this work, we show that in the case of bounded functions this quantity can be upper bounded by a polynomial in the degree of f (independently of dimension n), resolving affirmatively an open problem of Aaronson and Ambainis (ITCS 2011)....
Two well-studied closure operators for relations are based on primitive positive (p.p.) definitions and quantifier free p.p. definitions. The latter do however have limited expressiveness and the corresponding lattice of strong partial clones is uncountable. We consider implementations allowing polynomially many existentially quantified variables and obtain a dichotomy for co-clones where such implementations...
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