This paper describes a ternary partial-response signaling scheme for capacitively coupled chip-to-chip data transmission to increase data rate. Partial-response coding is known as a technique that allows high-speed transmission while using a limited frequency bandwidth, by allowing controlled intersymbol interference (ISI). Analysis and circuit simulation results are presented that compare this approach to two types of partial-response signaling, ternary duobinary (1+D) and dicode (1-D) signaling for capacitively coupled interface.
{"title":"A Ternary Partial-Response Signaling Scheme for Capacitively Coupled Interface","authors":"Y. Yuminaka, Kyohei Kawano","doi":"10.1109/ISMVL.2010.67","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.67","url":null,"abstract":"This paper describes a ternary partial-response signaling scheme for capacitively coupled chip-to-chip data transmission to increase data rate. Partial-response coding is known as a technique that allows high-speed transmission while using a limited frequency bandwidth, by allowing controlled intersymbol interference (ISI). Analysis and circuit simulation results are presented that compare this approach to two types of partial-response signaling, ternary duobinary (1+D) and dicode (1-D) signaling for capacitively coupled interface.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132557659","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}
The theory of Schauder hats is a beautiful and powerful tool for investigating, under several respects, the algebraic semantics of Łukasiewicz infinite-valued logic [CDM99],[MMM07], [Mun94], [P95]. As a notably application of the theory, the elements of the free n-generated MV-algebra, that constitutes the algebraic semantics of the n-variate fragment ofŁukasiewicz logic, are obtained as (t-conorm) monoidal combination of finitely many hats, which are in turn obtained through finitely many applications of an operation called starring, starting from a finite family of primitive hats. The aim of this paper is to extend this portion of the Schauder hats theory to the two-variable fragment of Hajek’s Basic logic. This step represents a non-trivial generalization of the one variable case studied in [AG05], [Mon00], and provides sufficient insight to capture the behaviour of the n-variable case for n ≥ 1.
{"title":"Schauder Hats for the Two-Variable Fragment of BL","authors":"S. Aguzzoli, S. Bova","doi":"10.1109/ISMVL.2010.14","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.14","url":null,"abstract":"The theory of Schauder hats is a beautiful and powerful tool for investigating, under several respects, the algebraic semantics of Łukasiewicz infinite-valued logic [CDM99],[MMM07], [Mun94], [P95]. As a notably application of the theory, the elements of the free n-generated MV-algebra, that constitutes the algebraic semantics of the n-variate fragment ofŁukasiewicz logic, are obtained as (t-conorm) monoidal combination of finitely many hats, which are in turn obtained through finitely many applications of an operation called starring, starting from a finite family of primitive hats. The aim of this paper is to extend this portion of the Schauder hats theory to the two-variable fragment of Hajek’s Basic logic. This step represents a non-trivial generalization of the one variable case studied in [AG05], [Mon00], and provides sufficient insight to capture the behaviour of the n-variable case for n ≥ 1.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127166244","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}
We study intervals $mathcal{I}(A)$ of partial clones whose total functions constitute a (total) clone A. In the Boolean case, we provide a complete classification of such intervals(according to whether the interval is finite or infinite), and determine the size of each finite interval $mathcal{I}(A)$.
{"title":"A Classification of Partial Boolean Clones","authors":"D. Lau, Karsten Schölzel","doi":"10.1109/ISMVL.2010.43","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.43","url":null,"abstract":"We study intervals $mathcal{I}(A)$ of partial clones whose total functions constitute a (total) clone A. In the Boolean case, we provide a complete classification of such intervals(according to whether the interval is finite or infinite), and determine the size of each finite interval $mathcal{I}(A)$.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127180109","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}
In several publications, the use of non-Abelian groups has been suggested as a method to derive compact representations of logic functions. The compactness has been measured in the number of product terms in the case of functional expressions and the number of nodes, the width, and the interconnections in the case of decision diagrams. In this paper, we discuss Fourier representations on finite non-Abelian groups in synthesis for regularity. The initial domain group for a logic function (binary or multiple-valued) is replaced by a non-Abelian group by encoding of variables. The function is then decomposed into matrix-valued Fourier coefficients, that are easy to implement as building blocks over a technological platform with regular structure. We point out that spectral representation of non-Abelian groups is capable of capturing regularities in functions and transferring them in the spectral domain. In many cases, weak regularities in the original domain are converted into much stronger regularities in the spectral domain due to the regular structure of unitary irreducible group representations upon which the Fourier expressions are based.
{"title":"Remarks on Applicability of Spectral Representations on Finite Non-Abelian Groups in the Design for Regularity","authors":"R. Stankovic, J. Astola, C. Moraga","doi":"10.1109/ISMVL.2010.64","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.64","url":null,"abstract":"In several publications, the use of non-Abelian groups has been suggested as a method to derive compact representations of logic functions. The compactness has been measured in the number of product terms in the case of functional expressions and the number of nodes, the width, and the interconnections in the case of decision diagrams. In this paper, we discuss Fourier representations on finite non-Abelian groups in synthesis for regularity. The initial domain group for a logic function (binary or multiple-valued) is replaced by a non-Abelian group by encoding of variables. The function is then decomposed into matrix-valued Fourier coefficients, that are easy to implement as building blocks over a technological platform with regular structure. We point out that spectral representation of non-Abelian groups is capable of capturing regularities in functions and transferring them in the spectral domain. In many cases, weak regularities in the original domain are converted into much stronger regularities in the spectral domain due to the regular structure of unitary irreducible group representations upon which the Fourier expressions are based.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130291254","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}
This paper proposes a new architecture for memory-based floating-point numeric function generators (NFGs). The design method uses piecewise-split edge-valued multi-valued decision diagrams (EVMDDs). To design NFGs with less memory size, we partition the domain of the floating-point function into segments, and represent the function using an EVMDD for each segment. By realizing each EVMDD with hardware, we obtain the floating-point NFG. This paper also presents an algorithm that partitions the domain by decomposing the edge-valued binary decision diagram(EVBDD) representing the whole floating-point function. Experimental results show that, for a single-precision floating-point function, our new NFG requires 40% to 65% less memory than any previous one. An advantage of our algorithm is that it can be applied to many different functions.
{"title":"Floating-Point Numeric Function Generators Based on Piecewise-Split EVMDDs","authors":"Shinobu Nagayama, Tsutomu Sasao, J. T. Butler","doi":"10.1109/ISMVL.2010.49","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.49","url":null,"abstract":"This paper proposes a new architecture for memory-based floating-point numeric function generators (NFGs). The design method uses piecewise-split edge-valued multi-valued decision diagrams (EVMDDs). To design NFGs with less memory size, we partition the domain of the floating-point function into segments, and represent the function using an EVMDD for each segment. By realizing each EVMDD with hardware, we obtain the floating-point NFG. This paper also presents an algorithm that partitions the domain by decomposing the edge-valued binary decision diagram(EVBDD) representing the whole floating-point function. Experimental results show that, for a single-precision floating-point function, our new NFG requires 40% to 65% less memory than any previous one. An advantage of our algorithm is that it can be applied to many different functions.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133480865","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}
Extending the work of Belnap [3], we continue our research on ESP structures, consisting of information sources and a processor which collects information from the sources, and develops it further using certain coherent rules. We examine the case of reasonable sources which provide coherent information, characterize the logic of a single reasonable source, and prove that the logics generated by ESP structures with reasonable sources coincide with the general source-processor logics described in our previous work. However, we show that, unlike the case of arbitrary sources, there are processor valuations in general ESP structures which cannot be obtained from any finite number of valuations defined by reasonable sources.
{"title":"Logics of Reasonable Information Sources","authors":"A. Avron, J. Ben-Naim, B. Konikowska","doi":"10.1109/ISMVL.2010.19","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.19","url":null,"abstract":"Extending the work of Belnap [3], we continue our research on ESP structures, consisting of information sources and a processor which collects information from the sources, and develops it further using certain coherent rules. We examine the case of reasonable sources which provide coherent information, characterize the logic of a single reasonable source, and prove that the logics generated by ESP structures with reasonable sources coincide with the general source-processor logics described in our previous work. However, we show that, unlike the case of arbitrary sources, there are processor valuations in general ESP structures which cannot be obtained from any finite number of valuations defined by reasonable sources.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122972238","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}
We analyze the existing encodings from MaxCSP into Partial MaxSAT, and report on a number of new insights that we have gained from our analysis, which can be summarized as follows: (i) the at-most-one (AMO) condition can be omitted in direct encodings from MaxCSP into Partial MaxSAT, and auxiliary variables are not needed; (ii) the sequential encoding of the cardinality constraint is, in fact, a reformulation of a regular encoding; (iii) the All Different constraint based on regular literals may be simplified; (iv) if we represent, in support encodings, the supporting values of a variable using intervals, then we can derive a genuine regular support encoding without exponential blowup; and (v) the Equal constraint admits a concise representation with regular signs.
{"title":"New Insights into Encodings from MaxCSP into Partial MaxSAT","authors":"Josep Argelich, Alba Cabiscol, I. Lynce, F. Manyà","doi":"10.1109/ISMVL.2010.17","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.17","url":null,"abstract":"We analyze the existing encodings from MaxCSP into Partial MaxSAT, and report on a number of new insights that we have gained from our analysis, which can be summarized as follows: (i) the at-most-one (AMO) condition can be omitted in direct encodings from MaxCSP into Partial MaxSAT, and auxiliary variables are not needed; (ii) the sequential encoding of the cardinality constraint is, in fact, a reformulation of a regular encoding; (iii) the All Different constraint based on regular literals may be simplified; (iv) if we represent, in support encodings, the supporting values of a variable using intervals, then we can derive a genuine regular support encoding without exponential blowup; and (v) the Equal constraint admits a concise representation with regular signs.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129357773","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}
For a fixed set $A$, an endoprimal monoid $M$ is a set of unary functions on $A$ which commute with some set $F$ of functions on $A$. A member of such $M$ defines an endomorphism on $F$. It is known to be hard to effectively characterize such endoprimal monoids. In this paper we present and discuss the ''witness lemma'' to study endoprimal monoids. Then, for the case where $|A|=3$, we verify two monoids to be endoprimal and then determine all endoprimal monoids having subsets of unary functions as their witnesses.
对于一个固定集合$ a $，一个内原单群$M$是$ a $上的一元函数的集合，它与$ a $上的函数集合$F$交换。这样的$M$中的一个元素在$F$上定义了一个自同态。众所周知，很难有效地表征这种内源一元虫。本文给出并讨论了研究内源一元群的“见证引理”。然后,| | = 3美元,我们验证两个独异点endoprimal然后确定所有endoprimal独异点在一元函数的子集作为证人。
{"title":"Endoprimal Monoids and Witness Lemma in Clone Theory","authors":"Hajime Machida, I. Rosenberg","doi":"10.1109/ISMVL.2010.44","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.44","url":null,"abstract":"For a fixed set $A$, an endoprimal monoid $M$ is a set of unary functions on $A$ which commute with some set $F$ of functions on $A$. A member of such $M$ defines an endomorphism on $F$. It is known to be hard to effectively characterize such endoprimal monoids. In this paper we present and discuss the ''witness lemma'' to study endoprimal monoids. Then, for the case where $|A|=3$, we verify two monoids to be endoprimal and then determine all endoprimal monoids having subsets of unary functions as their witnesses.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127076127","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}
Craig and deductive interpolation properties are investigated for uninorm based fuzzy logics. In particular, it is shown that for a restricted language, the only extensions of monoidal t-norm logic with Craig interpolation are classical logic, Godel logic, and three-valued Godel logic. Quantifier elimination in an appropriate language and the amalgamation, deductive interpolation and Craig interpolation properties are established for the logics based on idempotent residuated uninorms with an involutive negation.
{"title":"Interpolation Properties for Uninorm Based Logics","authors":"Enrico Marchioni, G. Metcalfe","doi":"10.1109/ISMVL.2010.46","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.46","url":null,"abstract":"Craig and deductive interpolation properties are investigated for uninorm based fuzzy logics. In particular, it is shown that for a restricted language, the only extensions of monoidal t-norm logic with Craig interpolation are classical logic, Godel logic, and three-valued Godel logic. Quantifier elimination in an appropriate language and the amalgamation, deductive interpolation and Craig interpolation properties are established for the logics based on idempotent residuated uninorms with an involutive negation.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127653896","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}
In this paper we show that the variety of SMV-algebras is generated by those algebras we call hyper real tensorial SMV-algebras. These are the SMV-algebras that can be defined by an MV-algebra A, and a hyper real state, i.e. a normalized and additive map s* : A → [0, 1]* .
{"title":"Generating the Variety of SMV-Algebras","authors":"A. Nola, T. Flaminio","doi":"10.1109/ISMVL.2010.34","DOIUrl":"https://doi.org/10.1109/ISMVL.2010.34","url":null,"abstract":"In this paper we show that the variety of SMV-algebras is generated by those algebras we call hyper real tensorial SMV-algebras. These are the SMV-algebras that can be defined by an MV-algebra A, and a hyper real state, i.e. a normalized and additive map s* : A → [0, 1]* .","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123692650","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}
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