Abhoy Kole, P. Rani, K. Datta, I. Sengupta, R. Drechsler
{"title":"Exact Synthesis of Ternary Reversible Functions Using Ternary Toffoli Gates","authors":"Abhoy Kole, P. Rani, K. Datta, I. Sengupta, R. Drechsler","doi":"10.1109/ISMVL.2017.51","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.51","url":null,"abstract":"Realization of logic functions using ternary reversible logic is known to requirelesser number of lines as compared to conventionalbinary reversible logic. This aspect of ternary reversible logic has motivated researchers to explore various synthesis approaches in the past. Existing synthesis methods require additional lines (called ancilla lines)for synthesis, which is expensive from the quantum implementation pointof view. There is no reported work for ternary reversible logic synthesisthat require the minimum possible number of gates and also lines. Thisclass of synthesis methods is called exact synthesis. In this paper two exact synthesis methods for ternary reversible logic have been proposed for the first time, one based on booleansatisfiability (SAT) and the other based on level-constrained heuristic search technique. A permutation representing a reversible ternary truth table is given as input, and a reversible circuit consisting ofgeneralized ternary Toffoli gates that implements the permutationis obtained as output. Experimental studies have been carried out on various randomly generatedternary reversible functions.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126217345","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}
Miguel Couceiro, L. Haddad, Victor Lagerqvist, Biman Roy
{"title":"On the Interval of Boolean Strong Partial Clones Containing Only Projections as Total Operations","authors":"Miguel Couceiro, L. Haddad, Victor Lagerqvist, Biman Roy","doi":"10.1109/ISMVL.2017.27","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.27","url":null,"abstract":"A strong partial clone is a set of partial operations closed under composition and containing all partial projections. Let X be the set of all Boolean strong partial clones whose total operations are the projections. This set is of practical interest since it induces a partial order on the complexity of NP-complete constraint satisfaction problems. In this paper we study X from the algebraic point of view, and prove that there exists two intervals in X, corresponding to natural constraint satisfaction problems, such that one is at least countably infinite and the other has the cardinality of the continuum.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133006727","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":"Error Bounded Exact BDD Minimization in Approximate Computing","authors":"Saman Fröhlich, Daniel Große, R. Drechsler","doi":"10.1109/ISMVL.2017.11","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.11","url":null,"abstract":"The Error Bounded Exact BDD Minimization (EBEBM) problem arises in approximate computing when one is trying to find a functional approximation with a minimal representation in terms of BDD size for a single output function with respect to a given error bound. In this paper we present an exact algorithm for EBEBM. This algorithm constructs a BDD representing all functions, which meet the restrictions induced by the given error bound. From this BDD we can derive an optimal solution. We compute the exact solutions for all functions with up to 4 variables and varying error bounds. Based on the results we demonstrate the benefit of our approachfor evaluating the quality of heuristic approximation algorithms.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126628273","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":"Fine-Grain Pipelined Reconfigurable VLSI Architecture Based on Multiple-Valued Multiplexer Logic","authors":"Katsuhiko Shimabukuro, M. Kameyama","doi":"10.1109/ISMVL.2017.45","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.45","url":null,"abstract":"This paper presents a novel bit-serial fine-grain pipelined reconfigurable VLSI architecture based on multiplexer logic to achieve high utilization of hardware resources and high throughput. A basic cell is constructed by a logic block composed of a 2-data-input multiplexer and a switch box for data transfer between adjacent logic blocks by 8-near neighborhood mesh network. A multiplexer merged with a latch function is effectively employed for efficient fine-grain pipelined operation. A systematic mapping method for pipelined bit-serial operations is proposed using a data flow graph. As an extension of the reconfigurable VLSI based on the binary multiplexer logic, we introduce linear summation in the data transfer between logic blocks. A 4-valued multiplexer directly controlled by the linear sum can be effectively utilized to reduce complexity of the switch box.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126823854","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":"Deep Learning for Autonomous Vehicles","authors":"B. Kisačanin","doi":"10.1109/ISMVL.2017.49","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.49","url":null,"abstract":"In this talk we discuss the latest developments in the art and science of autonomous driving. Deep Learning Networks have become indispensable in design and implementation of such systems. We will present the latest software and hardware tools for development and deployment of ever more computationally demanding DLNs used in self-driving cars. From DGX-1 supercomputer for training DLNs, to Drive PX 2, a scalable AI car computer platform for inference, and looking into the future, to the recently announced Xavier, an AI supercomputer on a chip for future autonomous vehicles, tools are now available for every part of a DLN lifecycle. We illustrate how the tools are being used already by showing some of the most recent results of Nvidia's own, end-to-end DLN for autonomous driving.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115081380","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}
Winston Haaswijk, Eleonora Testa, Mathias Soeken, G. Micheli
{"title":"Classifying Functions with Exact Synthesis","authors":"Winston Haaswijk, Eleonora Testa, Mathias Soeken, G. Micheli","doi":"10.1109/ISMVL.2017.44","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.44","url":null,"abstract":"Due to recent advances, constraint solvers have become efficient tools for synthesizing optimum Boolean circuits. We take advantage of this by showing how SAT based exact synthesis may be used as a method for finding minimum length Boolean chains. As opposed to other exact synthesis methods, ours may be easily parallelized, which we use to obtain a speedup of approximately 48 times. By combining our method with NPN canonization, we find for the first time the minimum length chains for all 4- and 5-input functions in terms of 3-input Boolean operators. Finally, we propose a hardware acceleration method for NPN canonization. It can be used to speed up NPN canonization in existing algorithms, and we believe it will allow us to find all 6-input NPN classes as well.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125420481","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}
M. Kvassay, E. Zaitseva, V. Levashenko, J. Kostolny
{"title":"Multi-valued Decision Diagrams for k-Out-of-n Three-State Systems","authors":"M. Kvassay, E. Zaitseva, V. Levashenko, J. Kostolny","doi":"10.1109/ISMVL.2017.38","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.38","url":null,"abstract":"One of the current issues in reliability analysis is investigation of complex systems that are composed of many components of variable nature. This variability implies that such systems have usually several performance levels and, therefore, they are modelled as Multi-State Systems (MSSs). Analysis of MSSs is a challenging task that consists of several steps. The principal task is a creation of such model that can be processed in a reasonable time. One of the possible ways for solving this task is application of tools related to multiple-valued logic. In this paper, we focus on a specific class of MSSs that is known as k-out-of-n systems. We develop a method that can be used for creation of a good model for this kind of MSSs. The presented method is based on multi-valued decision diagrams.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123978547","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 Systematic Design of Tamper-Resistant Galois-Field Arithmetic Circuits Based on Threshold Implementation with (d + 1) Input Shares","authors":"Rei Ueno, N. Homma, T. Aoki","doi":"10.1109/ISMVL.2017.35","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.35","url":null,"abstract":"This paper presents a systematic design of tamperresistantGalois-Field (GF) arithmetic circuits based on ThresholdImplementation (TI) where a secret variable is represented withmultiple variables, called shares, given by random numbers. TI isone of the countermeasures against Differential Power Analysis(DPA) on cryptographic hardware. The security order of TIdepends on the number of shares. The minimum number ofshares to be resistant dth-order DPA is said to be (d+1). Whilethe construction of GF arithmetic circuits of quadratic functionbased on TI with (d + 1) shares is known, it is not known howto construct other types of circuits based on it. In this paper, wepresent a generalization and systematic method of constructingthe TI with (d + 1) input shares for any kind of GF arithmeticcircuit in order to design a larger variety of tamper-resistantGF arithmetic circuits. We then apply the proposed method toa cryptographic hardware design in order to demonstrate its efficiency.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132171047","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":"Three Classes of Closed Sets of Monomials","authors":"Hajime Machida, J. Pantović","doi":"10.1109/ISMVL.2017.46","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.46","url":null,"abstract":"We consider three classes of monomials: unary, binary with at least one linear literal, and idempotent binary. A functionally closed set containing a unary monomial may or may not contain identity, and it can be generated by a singleton or by an arbitrary set of monomials. This induces four different classes of functionally closed sets of unary monomials. These classes are ordered by set inclusion and the emphasis is put on minimal, maximal, least and greatest elements. For binary monomials with at least one linear literal, we describe the structure of the set of clones generated by singletons. Finally, for idempotent binary monomials, we determine the least and the greatest element.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125807667","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":"Analog-to-Digital Converters Using Not Multi-level But Multi-bit Feedback Paths","authors":"T. Waho","doi":"10.1109/ISMVL.2017.30","DOIUrl":"https://doi.org/10.1109/ISMVL.2017.30","url":null,"abstract":"Conventional analog-to-digital converters (ADCs) with medium or high bit-resolution have a feedback path that connects a tentative digital output with the analog input to obtain a final digital output. Digital-to-analog converters (DACs) are used in the feedback path to generate the multi-level analog signal that is needed to process the feedback signal with the input signal in the analog domain. In this paper, Nyquist and oversampling ADCs using no DACs are presented, and their operations are proved by a behavior-model simulation. To remove the DACs from the feedback path and to replace the multi-level signal with the multi-bit one, a Hopfield artificial neural network is used with delta-sigma modulators as neurons. This new ADC architecture results in a circuit configuration more compact than that of conventional ADCs using the DAC.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128095487","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}