{"title":"Alternative Proof of Mulholland's Theorem and New Solutions to Mulholland Inequality","authors":"Milan Petrík, M. Navara, Peter Sarkoci","doi":"10.1109/ISMVL.2013.1","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.1","url":null,"abstract":"Mulholland inequality is a real functional inequality presented in 1950 in a paper by Mulholland as a generalization of the Minkowski inequality. In his paper, Mulholland has also provided a sufficient condition for the inequality to be satisfied. However, until now, it has remained an open problem whether this sufficient condition is also necessary. This paper investigates a geometric interpretation of Mulholland inequality and offers a class of functions satisfying the inequality which is strictly larger compared to the class delimited by the Mulholland's condition. Thus, it is proven that the condition is not necessary.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114496125","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":"Intersections with Slupecki Partial Clones on a Finite Set","authors":"L. Haddad, Karsten Schölzel","doi":"10.1109/ISMVL.2013.33","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.33","url":null,"abstract":"We study intersections of partial clones on the k-element set with k ≥ 2. More precisely we consider intersections of Slupecki partial clones with non-Slupecki maximal partial clones on k.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132578888","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":"An Area-Efficient Multiple-Valued Reconfigurable VLSI Architecture Using an X-Net","authors":"Xu Bai, M. Kameyama","doi":"10.1109/ISMVL.2013.13","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.13","url":null,"abstract":"An X-net is employed for simplifying interconnections and switch blocks of a multiple-valued reconfigurable VLSI (MV-RVLSI). One cell composed of a logic block and a switch block is connected to four adjacent \"X\" intersections by four one-bit switches. A multiple-valued X-net data transfer scheme is proposed to improve the utilization of the X-net, where two binary data can be transferred from two adjacent cells to one common adjacent cell simultaneously at each \"X\" intersection. To evaluate the MV-RVLSIs, a sum-of-absolute-differences operation is mapped onto a previous MV-RVLSI using an 8 nearest-neighbor mesh network (8-NNM) and the MV-RVLSI using the X-net, respectively. The area of the MV-RVLSI based on the multiple-valued X-net data transfer scheme is reduced to 73% and 84%, respectively, in comparison with those of the MVRVLSI using the 8-NNM and the MV-RVLSI based on a binary X-net data transfer scheme.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116234072","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":"Minimization of the Number of Edges in an EVMDD by Variable Grouping for Fast Analysis of Multi-State Systems","authors":"Shinobu Nagayama, Tsutomu Sasao, J. T. Butler","doi":"10.1109/ISMVL.2013.37","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.37","url":null,"abstract":"This paper proposes an algorithm to minimize the number of edges in an edge-valued multi-valued decision diagram (EVMDD) for fast analysis of multi-state systems. We minimize the number of edges by grouping multi-valued variables into larger-valued variables. By grouping multi-valued variables, we can also reduce the number of nodes. However, minimization of the number of nodes by grouping variables is not always effective for fast analysis of multi-state systems. On the other hand, minimization of the number of edges is effective. Experimental results show that the proposed algorithm for minimizing the number of edges reduces the number of edges by up to 15% and the number of nodes by up to 47%. This results in a speed-up of the analysis of multi-state systems by about three times.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126015999","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":"An Application of Autocorrelation Functions to Find Linear Decompositions for Incompletely Specified Index Generation Functions","authors":"Tsutomu Sasao","doi":"10.1109/ISMVL.2013.12","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.12","url":null,"abstract":"This paper shows that autocorrelation functions are useful to find the number of variables to represent incompletely specified index generation functions. It also shows a strategy to reduce the number of variables to represent incompletely specified index generation functions in the autocorrelation domain.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"46 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120977364","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 Natural Eight-Valued Reasoning","authors":"N. Kamide","doi":"10.1109/ISMVL.2013.43","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.43","url":null,"abstract":"It is known that many-valued paraconsistent logics are useful for expressing uncertain and inconsistency-tolerant reasoning in a wide range of Computer Science. Some four-valued and sixteen-valued paraconsistent logics have especially been well-studied. Some four-valued logics are not so fine-grained, and some sixteen-valued logics are enough fine-grained, but rather complex. In this paper, a natural eight-valued paraconsistent logic in between four-valued and sixteen-valued logics is introduced as a Gentzen-type sequent calculus. A triplet valuation semantics is introduced for this logic, and the completeness theorem for this semantics is proved. The cut-elimination theorem for this logic is proved, and this logic is shown to be decidable.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127015945","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":"Join Operations on Commutative BCK-Algebras with Condition (S)","authors":"M. Kawaguchi, Kouta Minami, M. Kondo","doi":"10.1109/ISMVL.2013.34","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.34","url":null,"abstract":"This research work focuses on join operations and some lattice structures in BCK-algebras. As the main result, the authors introduce a new definition of a join operation on commutative BCK-algebra with condition (S) instead of the boundedness property.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121732640","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":"Not Finitely Definable Partial Clones on a Finite Set","authors":"B. A. Romov","doi":"10.1109/ISMVL.2013.41","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.41","url":null,"abstract":"By establishing the relational theory of extendable partial clones on a finite set we describe infinite descending chains of partial clones whose intersection cannot be determined by a finite set of relations (we call them not finitely definable). A special type of such chains introduced in case of clones by I. Rosenberg (1972) as a generalization of two Post clones is investigated.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115183191","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":"Clones of Partial Cofunctions","authors":"Sebastian Kerkhoff, Friedrich Martin Schneider","doi":"10.1109/ISMVL.2013.18","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.18","url":null,"abstract":"We introduce and study clones of partial cofunctions on sets of arbitrary cardinality. In the process, we outline a general Galois theory similar to Pol-Inv, show some elementary results about the essential arity of clones of partial cofunctions, take a closer look at partial idempotent cofunctions, characterize all minimal clones of partial cofunctions, and show that the join of all minimal clones is the full clone (provided that the Axiom of Choice is assumed).","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122678450","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 Machine to Evaluate Decomposed Multi-Terminal Multi-Valued Decision Diagrams for Characteristic Functions","authors":"Hiroki Nakahara, Tsutomu Sasao, M. Matsuura","doi":"10.1109/ISMVL.2013.6","DOIUrl":"https://doi.org/10.1109/ISMVL.2013.6","url":null,"abstract":"A decomposed multi-terminal multi-valued decision diagrams for characteristic function(MTMDDs for CF) represents decomposed circuits. It can represent complex functions compactly. This paper shows a machine that evaluates decision diagrams. First, we introduce the decomposed MTMDDs for CF. Then, we consider two instructions to evaluate the decomposed MTMDDs for CF. Next, we show a machine that evaluates the decision diagrams. We compare that machine with embedded processors. As for the power-delay product, our machine running at 100 MHz is 60.84 times smaller than Nios II processor running at 100 MHz, and it is 18.66 times smaller than Atom N455 processor running at 1.67 GHz.","PeriodicalId":124947,"journal":{"name":"2013 IEEE 43rd International Symposium on Multiple-Valued Logic","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127122484","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}