For formal verification of hardware Satisfiability Modulo Theory (SMT) solvers are increasingly applied. Today's state-of-the-art SMT solvers use different techniques like term-rewriting, abstraction, or bit-blasting. The performance does not only depend on the underlying decision problem but also on the encoding of the original problem into an SMT instance. In this work, encodings for cardinality constraints in SMT are investigated. Three different encodings are considered: an adder network, an encoding with multiplexors, and a newly proposed encoding with shifters. The encodings are analyzed with respect to size and complexity. The experimental evaluation on debugging instances that contain cardinality constraints shows the strong influence of the encoding on the resulting run-times.
{"title":"Evaluation of Cardinality Constraints on SMT-Based Debugging","authors":"André Sülflow, R. Wille, G. Fey, R. Drechsler","doi":"10.1109/ISMVL.2009.28","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.28","url":null,"abstract":"For formal verification of hardware Satisfiability Modulo Theory (SMT) solvers are increasingly applied. Today's state-of-the-art SMT solvers use different techniques like term-rewriting, abstraction, or bit-blasting. The performance does not only depend on the underlying decision problem but also on the encoding of the original problem into an SMT instance. In this work, encodings for cardinality constraints in SMT are investigated. Three different encodings are considered: an adder network, an encoding with multiplexors, and a newly proposed encoding with shifters. The encodings are analyzed with respect to size and complexity. The experimental evaluation on debugging instances that contain cardinality constraints shows the strong influence of the encoding on the resulting run-times.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"10 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126036868","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}
Many types of fuzzy truth values, numerical, interval, triangular, and trapezoid truth values, have been proposed and studied about their mathematical properties. It is the characteristic that they are convex fuzzy truth values. Recently, a new type of fuzzy truth values, which we call multi-interval truth values, have been proposed. A characteristic feature of multi-interval truth values is that some of them are not convex. The conventional operations min, max and x mapsto 1-x$ on the unit interval [0, 1] can be expanded into those on the set of multi-interval truth values. These operations are denoted as $land$, $sqcup$, $bar{~~}$, respectively. Then, this paper first shows that $(S, land, sqcup, bar{~~}, mathbf{0}, mathbf{1})$ is a de Morgan bisemilattice. Next, this paper focuses on functions that are expressed by logic formulas, where a logic formula is composed of variables on multi-interval truth values, and the operations $sqcup$, $land$ and $bar{~~}$. Necessary conditions for a function on multi-interval truth values to be expressed by a logic formula are clarified.
{"title":"Non-convex Fuzzy Truth Values and De Morgan Bisemilattices","authors":"N. Takagi","doi":"10.1109/ISMVL.2009.34","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.34","url":null,"abstract":"Many types of fuzzy truth values, numerical, interval, triangular, and trapezoid truth values, have been proposed and studied about their mathematical properties. It is the characteristic that they are convex fuzzy truth values. Recently, a new type of fuzzy truth values, which we call multi-interval truth values, have been proposed. A characteristic feature of multi-interval truth values is that some of them are not convex. The conventional operations min, max and x mapsto 1-x$ on the unit interval [0, 1] can be expanded into those on the set of multi-interval truth values. These operations are denoted as $land$, $sqcup$, $bar{~~}$, respectively. Then, this paper first shows that $(S, land, sqcup, bar{~~}, mathbf{0}, mathbf{1})$ is a de Morgan bisemilattice. Next, this paper focuses on functions that are expressed by logic formulas, where a logic formula is composed of variables on multi-interval truth values, and the operations $sqcup$, $land$ and $bar{~~}$. Necessary conditions for a function on multi-interval truth values to be expressed by a logic formula are clarified.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117017927","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}
R. Sakashita, A. Uchinuno, K. Kamiizumi, Keiko Tei, N. Awaya
The authors have been developing a tool for measuring for the quality of nursing care since 1993. This tool consisted of three dimensions: structure, process, and outcome. Each dimension was constructed from measurements of six domains into which the applicants responses were previously ¿categorized, such as "understanding individuality", "patient empowerment", "family care", "direct care", "medical team coordination " and "incident prevention". It has been developed and posted on a web site for gathering data from, and returning feedback to the participants’ units for the quality improvement of nursing. In this study, a fuzzy recommendation system for the feedback was developed through an expert panel then evaluated by participants.
{"title":"Web-Based Nursing Care Quality Improvement System with Fuzzy Recommendation System","authors":"R. Sakashita, A. Uchinuno, K. Kamiizumi, Keiko Tei, N. Awaya","doi":"10.1109/ISMVL.2009.22","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.22","url":null,"abstract":"The authors have been developing a tool for measuring for the quality of nursing care since 1993. This tool consisted of three dimensions: structure, process, and outcome. Each dimension was constructed from measurements of six domains into which the applicants responses were previously ¿categorized, such as \"understanding individuality\", \"patient empowerment\", \"family care\", \"direct care\", \"medical team coordination \" and \"incident prevention\". It has been developed and posted on a web site for gathering data from, and returning feedback to the participants’ units for the quality improvement of nursing. In this study, a fuzzy recommendation system for the feedback was developed through an expert panel then evaluated by participants.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127241725","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 studies sets of hyper-operations preserving relations on power set without emptyset. For a particular property of a relation, such a set is hyperclone. We consider relations having total part exactly from Rosenberg's classes of relations. By investigating nontrivial equivalence relations, central relations and regular relations as total part, we show that sets of hyper-operations preserving such hyper-relations are maximal hyperclones.
{"title":"Hyperclones Determined by Total-Parts of Hyper-relations","authors":"Hajime Machida, J. Pantović","doi":"10.1109/ISMVL.2009.50","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.50","url":null,"abstract":"This paper studies sets of hyper-operations preserving relations on power set without emptyset. For a particular property of a relation, such a set is hyperclone. We consider relations having total part exactly from Rosenberg's classes of relations. By investigating nontrivial equivalence relations, central relations and regular relations as total part, we show that sets of hyper-operations preserving such hyper-relations are maximal hyperclones.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123957899","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}
MaxSAT solvers have made tremendous progress in terms of performance in recent years. However, there has not been parallel progress in the generation of challenging benchmarks for studying the scaling behavior of solvers, and comparing their performance. Most experimental investigations only include, besides the standard MaxkSAT instances, the sets of individual instances submitted to the MaxSAT evaluations held so far. The problem with many of the latter instances is that they are becoming easy for modern solvers, and do not allow to analyse the scaling behavior. To cope with that problem, we propose several newgenerators of MaxSAT instances, which produce pure random instances as well as more realistic, structured instances.Moreover, we report on an experimental investigation with the aim of analysing the behavior of some of the fastest MaxSAT solvers when solving instances produced with the new generators. Our empirical results provide a new testbed of challenging benchmarks, as well as insights into the hardness nature of MaxSAT.
{"title":"Generating Hard Instances for MaxSAT","authors":"R. Béjar, Alba Cabiscol, F. Manyà, Jordi Planes","doi":"10.1109/ISMVL.2009.58","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.58","url":null,"abstract":"MaxSAT solvers have made tremendous progress in terms of performance in recent years. However, there has not been parallel progress in the generation of challenging benchmarks for studying the scaling behavior of solvers, and comparing their performance. Most experimental investigations only include, besides the standard MaxkSAT instances, the sets of individual instances submitted to the MaxSAT evaluations held so far. The problem with many of the latter instances is that they are becoming easy for modern solvers, and do not allow to analyse the scaling behavior. To cope with that problem, we propose several newgenerators of MaxSAT instances, which produce pure random instances as well as more realistic, structured instances.Moreover, we report on an experimental investigation with the aim of analysing the behavior of some of the fastest MaxSAT solvers when solving instances produced with the new generators. Our empirical results provide a new testbed of challenging benchmarks, as well as insights into the hardness nature of MaxSAT.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117277682","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 endomorphisms of a universal algebra on a universe A form a monoid of selfmaps on A. Such monoids, called endoprimal monoids, are special and rare. In this paper we study the first interesting case of a 3-element set A. In the lattice of inclusion-ordered endoprimal monoids we find three maximal endoprimal monoids. This knowledge allows us to conclude that many large monoids are not endoprimal.
{"title":"On Endoprimal Monoids in Clone Theory","authors":"Hajime Machida, I. Rosenberg","doi":"10.1109/ISMVL.2009.53","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.53","url":null,"abstract":"The endomorphisms of a universal algebra on a universe A form a monoid of selfmaps on A. Such monoids, called endoprimal monoids, are special and rare. In this paper we study the first interesting case of a 3-element set A. In the lattice of inclusion-ordered endoprimal monoids we find three maximal endoprimal monoids. This knowledge allows us to conclude that many large monoids are not endoprimal.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127518717","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 framework that improves reversible logic synthesis by employing a dynamically determined variable order for quantum multiple-valued decision diagrams (QMDD). We demonstrate our approach through augmentation of the Miller-Maslov-Dueck (MMD) algorithm that processes the complete function specification in lexicographical order with our technique. We represent and minimize the complete specification with the QMDD and then synthesize the function specification based on the minimized variable order. The framework produces significantly smaller reversible circuits in many cases. Experimental results also show the effectiveness of using the QMDD size as a measure of the complexity of MVL and binary reversible circuits.
{"title":"On the Guidance of Reversible Logic Synthesis by Dynamic Variable Reordering","authors":"D. Y. Feinstein, M. Thornton","doi":"10.1109/ISMVL.2009.31","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.31","url":null,"abstract":"This paper proposes a framework that improves reversible logic synthesis by employing a dynamically determined variable order for quantum multiple-valued decision diagrams (QMDD). We demonstrate our approach through augmentation of the Miller-Maslov-Dueck (MMD) algorithm that processes the complete function specification in lexicographical order with our technique. We represent and minimize the complete specification with the QMDD and then synthesize the function specification based on the minimized variable order. The framework produces significantly smaller reversible circuits in many cases. Experimental results also show the effectiveness of using the QMDD size as a measure of the complexity of MVL and binary reversible circuits.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133973931","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}
Satyendra R. Datla, M. Thornton, Luther Hendrix, Dave Henderson
Multiple Valued Logic (MVL) has been gaining popularity and practical applications. In addition to the standard MVL benefits, quaternary logic offers the benefit of easy interfacing to binary logic due to the fact that the radix 4=22 allows for simple encoding/decoding circuits. Quaternary cells based on the Supplementary Symmetrical Logic Circuit Structure (SUSLOC) [2] are modeled and used for our adder circuit structures. Several different adder configurations are designed and modeled using the basic quaternary gates and are modeled with the SystemVerilog modeling language. Different adder configurations are compared for their size and estimated logic depth for area and performance estimation and compared with their binary counterparts.
多值逻辑(Multiple value Logic, MVL)已逐渐得到普及和实际应用。除了标准的MVL优势之外，由于基数4=22允许简单的编码/解码电路，四进制逻辑还提供了与二进制逻辑轻松接口的优势。基于补充对称逻辑电路结构(SUSLOC)[2]的第四元胞被建模并用于我们的加法器电路结构。使用基本的四元门设计和建模了几种不同的加法器配置，并用SystemVerilog建模语言进行了建模。对不同的加法器配置进行了尺寸和估计逻辑深度的比较，以进行面积和性能估计，并与二进制加法器进行了比较。
In this paper we present the synthesis process of quantum finite state machines for sequence detection based on the synthesis of quantum sequential circuits. Such machines have many applications for instance in robotics. We show the relation between the quantum circuit and the natural ability of quantum systems to retain the quantum state. We consider cases where a single qubit in a circuit represents a quantum state and another is used as the input qubit. We analyze some of the well known circuits as sequence detectors and describe their behaviors. We show that the standard quantum logic synthesis can be used for both the synthesis of quantum circuits as well as for quantum finite state machines used as sequence detectors.
{"title":"Quantum Finite State Machines as Sequential Quantum Circuits","authors":"M. Lukac, M. Perkowski","doi":"10.1109/ISMVL.2009.46","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.46","url":null,"abstract":"In this paper we present the synthesis process of quantum finite state machines for sequence detection based on the synthesis of quantum sequential circuits. Such machines have many applications for instance in robotics. We show the relation between the quantum circuit and the natural ability of quantum systems to retain the quantum state. We consider cases where a single qubit in a circuit represents a quantum state and another is used as the input qubit. We analyze some of the well known circuits as sequence detectors and describe their behaviors. We show that the standard quantum logic synthesis can be used for both the synthesis of quantum circuits as well as for quantum finite state machines used as sequence detectors.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133283587","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}
S. Kasai, Y. Shiratori, Kensuke Miura, Nan-Jian Wu
Simple and compact multi-path switching devices for multi-valued decision diagram (MDD)-based logic circuits are designed, fabricated and characterized. The devices switch multiple exit branches for electrons entering from an entry branch, according to multi-valued input. The switching function is implemented by dual gating on multiple nanowires with different threshold voltages. The gate threshold voltage is controlled by precise design of gate structures and sizes in nanometer scale. The operation principle of the device is described using a simple analytical model. Ternary-path switching devices are demonstrated using AlGaAs/GaAs etched nanowire junctions together with nanometer-scale Schottky wrap gates (WPGs) and in-plane gates (IPGs).
{"title":"Multi-path Switching Device Utilizing a Multi-terminal Nanowire Junction for MDD-Based Logic Circuit","authors":"S. Kasai, Y. Shiratori, Kensuke Miura, Nan-Jian Wu","doi":"10.1109/ISMVL.2009.43","DOIUrl":"https://doi.org/10.1109/ISMVL.2009.43","url":null,"abstract":"Simple and compact multi-path switching devices for multi-valued decision diagram (MDD)-based logic circuits are designed, fabricated and characterized. The devices switch multiple exit branches for electrons entering from an entry branch, according to multi-valued input. The switching function is implemented by dual gating on multiple nanowires with different threshold voltages. The gate threshold voltage is controlled by precise design of gate structures and sizes in nanometer scale. The operation principle of the device is described using a simple analytical model. Ternary-path switching devices are demonstrated using AlGaAs/GaAs etched nanowire junctions together with nanometer-scale Schottky wrap gates (WPGs) and in-plane gates (IPGs).","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114964213","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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