Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

2020 ◽  
Keyword(s):  
Theory Of Computing

scholarly journals On Computing Multilinear Polynomials Using Multi- r -ic Depth Four Circuits

2021 ◽  
Vol 13 (3) ◽  
pp. 1-21
Author(s):  
Suryajith Chillara
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Complexity Measure ◽  
Natural Question ◽  
Multilinear Polynomial ◽  
Arithmetic Circuit ◽  
Theory Of Computing ◽  
Small Constant ◽  
Multilinear Polynomials ◽  
The Individual

In this article, we are interested in understanding the complexity of computing multilinear polynomials using depth four circuits in which the polynomial computed at every node has a bound on the individual degree of r ≥ 1 with respect to all its variables (referred to as multi- r -ic circuits). The goal of this study is to make progress towards proving superpolynomial lower bounds for general depth four circuits computing multilinear polynomials, by proving better bounds as the value of r increases. Recently, Kayal, Saha and Tavenas (Theory of Computing, 2018) showed that any depth four arithmetic circuit of bounded individual degree r computing an explicit multilinear polynomial on n O (1) variables and degree d must have size at least ( n / r 1.1 ) Ω(√ d / r ) . This bound, however, deteriorates as the value of r increases. It is a natural question to ask if we can prove a bound that does not deteriorate as the value of r increases, or a bound that holds for a larger regime of r . In this article, we prove a lower bound that does not deteriorate with increasing values of r , albeit for a specific instance of d = d ( n ) but for a wider range of r . Formally, for all large enough integers n and a small constant η, we show that there exists an explicit polynomial on n O (1) variables and degree Θ (log 2 n ) such that any depth four circuit of bounded individual degree r ≤ n η must have size at least exp(Ω(log 2 n )). This improvement is obtained by suitably adapting the complexity measure of Kayal et al. (Theory of Computing, 2018). This adaptation of the measure is inspired by the complexity measure used by Kayal et al. (SIAM J. Computing, 2017).

Theory of computing

1997 ◽  
Vol 28 (3) ◽  
pp. 100-102
Author(s):  
Oded Goldreich ◽  
Avi Wigderson
Keyword(s):  
Theory Of Computing

scholarly journals A New Approach to Computing Using Informons and Holons: Towards a Theory of Computing Science

2019 ◽  
Vol 25 (4) ◽  
pp. 1173-1201 ◽  
Author(s):  
F. David de la Peña ◽  
Juan A. Lara ◽  
David Lizcano ◽  
María Aurora Martínez ◽  
Juan Pazos
Keyword(s):  
New Approach ◽  
Theory Of Computing ◽  
Computing Science

NSF Report: Theory of Computing Program

1997 ◽  
Vol 28 (4) ◽  
pp. 31
Author(s):  
Zeke Zalcstein
Keyword(s):  
Theory Of Computing

scholarly journals Modeling Computing Devices and Processes by Information Operators

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 18
Author(s):  
Mark Burgin ◽  
Gordana Dodig-Crnkovic
Keyword(s):  
Operator Theory ◽  
Computer Architectures ◽  
General Context ◽  
Theoretical Studies ◽  
Operator Approach ◽  
Operator Representation ◽  
Practical Applications ◽  
Theory Of Computing

The concept of operator is exceedingly important in many areas as a tool of theoretical studies and practical applications. Here, we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, networks, and processes. In particular, the operator approach allows for the solving of many computing problems in a more general context of operating spaces. In addition, operator representation of computing devices and their networks allows for the construction of a variety of operator compositions and the development of new schemas of computation as well as network and computer architectures using operations with operators. Besides, operator representation allows for the efficient application of the axiomatic technique for the investigation of computation.

Aspects of Intelligence in an "SP" Database System

2009 ◽  
pp. 725-754
Author(s):  
J. Gerard Wolff
Keyword(s):  
Pattern Recognition ◽  
Information Retrieval ◽  
Natural Language ◽  
Unsupervised Learning ◽  
Probabilistic Reasoning ◽  
Database System ◽  
Theory Of Computing ◽  
New Knowledge ◽  
Database Models

This chapter describes some of the kinds of “intelligence” that may be exhibited by an intelligent database system based on the SP theory of computing and cognition. The chapter complements an earlier paper on the SP theory as the basis for an intelligent database system (Wolff, forthcoming b) but it does not depend on a reading of that earlier paper. The chapter introduces the SP theory and its main attractions as the basis for an intelligent database system: that it uses a simple but versatile format for diverse kinds of knowledge, that it integrates and simplifies a range of AI functions, and that it supports established database models when that is required. Then with examples and discussion, the chapter illustrates aspects of “intelligence” in the system: pattern recognition and information retrieval, several forms of probabilistic reasoning, the analysis and production of natural language, and the unsupervised learning of new knowledge.

scholarly journals Special issue: 35th Annual ACM Symposium on Theory of Computing

2004 ◽  
Vol 69 (3) ◽  
pp. 305
Author(s):  
Sanjeev Khanna ◽  
Aravind Srinivasan
Keyword(s):  
Special Issue ◽  
Theory Of Computing
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