{"title":"Commutation for Functions of Small Arity Over a Finite Set","authors":"Hajime Machida, I. Rosenberg","doi":"10.1109/ISMVL.2018.00023","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00023","url":null,"abstract":"Commutation is defined for multi-variable functions on a finite base set. For a set F of functions the centralizer F* of F is the set of functions which commute with all functions in F. For a function f a minor of f is a function obtained from f by iden- tifying some of its variables. An important observation is that the centralizer f* of f is a subclone of the centralizer of any minor of f, which motivates the study of the centralizers of functions of small arity. In this paper we determine the centralizers of all 2-variable functions over the two-element set. Then, as a generalization of AND on the 2-element set we consider the function Min on the k-element set, k > 1, and characterize the centralizer of Min using a term from lattice theory.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125968003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"One Class of Maximal Binary Monomials","authors":"Hajime Machida, J. Pantović","doi":"10.1109/ISMVL.2018.00022","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00022","url":null,"abstract":"The lattice of closed sets of monomials generated by a monomial of the form xy t over a finite field GF(k) is isomorphic to the lattice of divisors of k-1. If a monomial xy t generates a maximal element in that lattice, does it also generate a maximal element in the poset of closed sets generated by singleton binary monomials? This is the question studied in this paper. We have proven that over some finite fields xy 2 is a unique such monomial.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128109818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Realization of Arithmetic Operators Based on Stochastic Number Frequency Signal Representation","authors":"M. M. A. Taha, M. Perkowski","doi":"10.1109/ISMVL.2018.00045","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00045","url":null,"abstract":"This paper presents new arithmetic operators based on frequency signal representation. The results obtained when testing/simulating the arithmetic operators circuits with ModelSim PE student 10.4a are also shown. Such operations are similar but not the same as those in Stochastic Number Representations (SNRs). Multiplica- tion, division, roots and others are discussed, realized and simulated. The future goal is to realize them with memristors for a new type of a massively parallel CMOS- memristor FPGA, as memristors offer low-power, parallel operations.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121208298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Design of a Low-Power MTJ-Based True Random Number Generator Using a Multi-voltage/Current Converter","authors":"Shogo Mukaida, N. Onizawa, T. Hanyu","doi":"10.1109/ISMVL.2018.00035","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00035","url":null,"abstract":"In this paper, we introduce a multi-V/I converter for low-power true random number generator (TRNG) using a three-terminal magnetic tunnel junction (MTJ) device. As MTJ devices are probabilistically switched by current, the desired probability of 50% is digitally controlled by digital-to-analog (D/A) and V/I converters. In the conventional MTJ-based TRNG a highly accurate (and large-power) D/A is required to be tolerate to large temperature variation of MTJ devices. By changing the characteristics dynamically according to the temperature variation, the proposed circuit can reduce the bit precision of the D/A converter while generating the quality of random number as the conventional V/I converter. The circuit is designed with a 65nm CMOS/three-terminal MTJ model, and the simulation is carried out using HSPICE. As a result, the number of bits of the D/A converter is reduced from 10 bits to 7 bits.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114840112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebra of Transient States of Postan Signals","authors":"Maciej Rudziecki","doi":"10.1109/ISMVL.2018.00046","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00046","url":null,"abstract":"The m-element Post algebra of m-order, m≥2, is successfully used to describe the steady states of Postan signals in multiple-valued switching circuits. The quasi-Post algebra is introduced to describe both the steady and non-steady states of the Postan signals the similar way as the three-element quasi-Boolean algebra describes the steady and non-steady states of the Boolean signals. The quasi-Post algebra is constructed in such a way that the Post algebra is the subalgebra of the quasi-Post algebra. Operations on steady and transient states of Postan signals are defined and properties of those operations are presented. The algebraic functions of the quasi-Post algebra can be used to study transient states and hazards in multiple-valued combinational logic networks.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116279265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Ternary Weight Binary Input Convolutional Neural Network: Realization on the Embedded Processor","authors":"H. Yonekawa, Shimpei Sato, Hiroki Nakahara","doi":"10.1109/ISMVL.2018.00038","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00038","url":null,"abstract":"In image recognition, techniques using a convolutional neural network (CNN) have been extensively studied and are widely used in various applications, such as a handwritten character recognition, a face recognition, a scene determination, and an object recognition. It has an enormous amount of computational complexity and internal parameters, and it is often implemented in high-performance GPUs. However, the embedded system requires real-time image recognition with a low-power consumption. In such systems, a binarized CNN has been proposed for the embedded system. It can achieve efficient implementation by restricting the values that the parameters inside CNN treating -1 and +1, and low bit precision of operations and memory. In the paper, we extend to a ternary weight binary input CNN to further increase its performance with a low-performance embedded processor. In the ternarized CNN, values that internal weight can take -1, +1 and 0, where zero weight can be realized by a skip computation. Since the number of possible states of the ternarized CNN is larger than that of the binarized CNN, high recognition accuracy can be obtained. Furthermore, we study an optimal training algorithm in the ternarized CNN and show the results by computer experiment. Comparison with the binarized CNN, as for the ARM processor, the ternary weight CNN was 8.13 times faster than the binary weight one.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115230294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a Memory-Based Realization of Sparse Multiple-Valued Functions","authors":"Tsutomu Sasao","doi":"10.1109/ISMVL.2018.00017","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00017","url":null,"abstract":"This paper presents multi-valued (MV) functions, which are generalizations of index generation functions and switching functions. First, an efficient memory-based realization of sparse MV functions, where the number of specified combinations is much smaller than the number of possible input combinations, is presented. Then, a formula for the expected number of variables to represent random sparse MV functions is derived. Finally, the theoretical analysis is compared with the experimental results.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131168501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Logic Design Using Memristors: An Emerging Technology","authors":"S. Shirinzadeh, K. Datta, R. Drechsler","doi":"10.1109/ISMVL.2018.00029","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00029","url":null,"abstract":"This paper provides an introduction to memristor, which is considered as the fourth circuit element along with resistor, inductor and capacitor. Memristors possess some unique properties, i.e. it can change the resistance under voltage control and can retain its value even after the voltage is withdrawn. Another property of memristors is their small feature size which makes them useful for design of ultra-compact memory systems. In addition, the resistive switching property of memristors allows to execute logic primitives and thus can also be used for implementing logic functions using various logic design styles studied in this paper. The paper also discusses memristor fabrication, circuit models, methods for implementing logic functions, and the various computing methodologies that can be used viz. nearmemory computing and in-memory computing.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"9 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130512309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Beyond Bits: A Quaternary FPGA Architecture Using Multi-Vt Multi-Vdd FDSOI Devices","authors":"S. Chaudhuri","doi":"10.1109/ISMVL.2018.00015","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00015","url":null,"abstract":"In this article we present the architecture of a quaternary FPGA, its implementation in FDSOI technology, and a comparison with binary architectures based on VPR. We discuss the transistor level design of LUTs, Flip-Flops, Muxes, and multi-valued buffer circuits exploiting the capability of FDSOI technology to modify threshold voltages. We present I/O elements of such an FPGA with binary to quaternary translators and a new technique to reduce global routing by combining clock and reset on the same wire. We model the area, delay and power consumption of the quaternary FPGA architecture in VPR. We compare the implementation of very simple arithmetic benchmarks with equivalent two-valued FPGA architectures in VPR. We show that, it is possible to achieve upto 15% reduction in transistor area, and 10% reduction in critical path delay.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124570619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Surhonne, Debjyoti Bhattacharjee, A. Chattopadhyay
{"title":"Synthesis of Multi-valued Literal Using Lukasiewicz Logic","authors":"A. Surhonne, Debjyoti Bhattacharjee, A. Chattopadhyay","doi":"10.1109/ISMVL.2018.00043","DOIUrl":"https://doi.org/10.1109/ISMVL.2018.00043","url":null,"abstract":"The synthesis of multi-valued combinational functions is well-studied topic, albeit less compared to the synthesis of two-valued logic families. The synthesis of multi-valued functions consists of bi-decomposition or functional decomposition of the given target function to obtain a multilevel network comprising of min and max gates. Synthesis tools, such as YADE and those based on Multiple-Valued Decision Diagrams make the implicit assumption regarding the availability of literals or CASE operator, while focusing on the optimization of the logic network solely based on the min and max gates. However, a literal cannot be assumed to exist as a primitive in a multi-valued logic system and therefore, renders it difficult for one to directly apply the existing synthesis flows in practical settings [1]. We address this important gap in MVL synthesis flows. Our target multivalued logic is £ukasiewicz logic, which supports implication and negation. We derive literals and CASE operators using these primitives, and propose a heuristic algorithm to synthesize it automatically. Our techniques are implemented as an extension in the YADE tool. Our experimental studies on a wide range of benchmarks reveal that an average overhead of 216% in terms of number implication gates, along with 55% increase in the number of levels is encountered, in contrast to a synthesis flow that assumes existence of literals.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134536255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}