The formal theory of division in arithmetical algebras reconstructs fractions as syntactic objects called fracterms. Basic to calculation, is the simplification of fracterms to fracterms with one division operator, a process called fracterm attening. We consider the equational axioms of a calculus for calculating with fracterms to determine what is necessary and sufficient for the fracterm calculus to allow fracterm flattening. For computation, arithmetical algebras require operators to be total for which there are several semantical methods. It is shown under what constraints up to isomorphism, the unique total and minimal enlargement of a field Q(div) of rational numbers equipped with a partial division operator div has fracterm attening.
{"title":"Which Arithmetical Data Types Admit Fracterm Flattening?","authors":"J. Bergstra, J. V. Tucker","doi":"10.7561/SACS.2022.1.87","DOIUrl":"https://doi.org/10.7561/SACS.2022.1.87","url":null,"abstract":"The formal theory of division in arithmetical algebras reconstructs fractions as syntactic objects called fracterms. Basic to calculation, is the simplification of fracterms to fracterms with one division operator, a process called fracterm attening. We consider the equational axioms of a calculus for calculating with fracterms to determine what is necessary and sufficient for the fracterm calculus to allow fracterm flattening. For computation, arithmetical algebras require operators to be total for which there are several semantical methods. It is shown under what constraints up to isomorphism, the unique total and minimal enlargement of a field Q(div) of rational numbers equipped with a partial division operator div has fracterm attening.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129211210","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}
These reflections are distilled from my experience as the editor-in-chief of the journal ‘Scientific Annals of Computer Science’.
这些思考是从我作为《计算机科学科学年鉴》杂志主编的经历中提炼出来的。
{"title":"Reflections on a Scientific Journal","authors":"Gabriel Ciobanu","doi":"10.7561/SACS.2022.1.1","DOIUrl":"https://doi.org/10.7561/SACS.2022.1.1","url":null,"abstract":"These reflections are distilled from my experience as the editor-in-chief of the journal ‘Scientific Annals of Computer Science’.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131687592","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}
Using the conceptual analysis of instruction sequence faults, failures, and defects as developed by the author in [10] and [12], a survey of testing is developed as an extension of a theory of instruction sequences. An attempt is made to develop a consistent terminology regarding instruction sequence testing while taking into account the literature on software testing at large.
{"title":"A Survey of Testing for Instruction Sequence Theory","authors":"J. Bergstra","doi":"10.7561/SACS.2022.1.5","DOIUrl":"https://doi.org/10.7561/SACS.2022.1.5","url":null,"abstract":"Using the conceptual analysis of instruction sequence faults, failures, and defects as developed by the author in [10] and [12], a survey of testing is developed as an extension of a theory of instruction sequences. An attempt is made to develop a consistent terminology regarding instruction sequence testing while taking into account the literature on software testing at large.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134244791","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 prove that almost all the properties of quantum-MV algebras are verified by orthomodular algebras, the new algebras introduced in a previous paper. We put a special insight on transitive antisymmetric orthomodular (taOM) algebras, generalizations of MV algebras. We make the connection with IMTL and NM algebras. In memoriam Dragos. Vaida (1933 – 2020)
{"title":"On Quantum-MV Algebras - Part I: The Orthomodular Algebras","authors":"A. Iorgulescu","doi":"10.7561/SACS.2021.2.163","DOIUrl":"https://doi.org/10.7561/SACS.2021.2.163","url":null,"abstract":"We prove that almost all the properties of quantum-MV algebras are verified by orthomodular algebras, the new algebras introduced in a previous paper. We put a special insight on transitive antisymmetric orthomodular (taOM) algebras, generalizations of MV algebras. We make the connection with IMTL and NM algebras. In memoriam Dragos. Vaida (1933 – 2020)","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114719870","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 map that can be rotated, we consider the following problem. There are a number of feature points on the map, each having a geometric object as a label. The goal is to find the largest subset of these labels such that when the map is rotated and the labels remain vertical, no two labels in the subset intersect. We show that, even if the labels are vertical bars of zero width, this problem remains NP-hard, and present a polynomial approximation scheme for solving it. We also introduce a new variant of the problem for vertical labels of zero width, in which any label that does not appear in the output must be coalesced with a label that does. Coalescing a subset of the labels means to choose a representative among them and set its label height to the sum of the individual label heights.
{"title":"Maximizing the Number of Visible Labels on a Rotating Map","authors":"A. Rudi","doi":"10.7561/SACS.2021.2.293","DOIUrl":"https://doi.org/10.7561/SACS.2021.2.293","url":null,"abstract":"For a map that can be rotated, we consider the following problem. There are a number of feature points on the map, each having a geometric object as a label. The goal is to find the largest subset of these labels such that when the map is rotated and the labels remain vertical, no two labels in the subset intersect. We show that, even if the labels are vertical bars of zero width, this problem remains NP-hard, and present a polynomial approximation scheme for solving it. We also introduce a new variant of the problem for vertical labels of zero width, in which any label that does not appear in the output must be coalesced with a label that does. Coalescing a subset of the labels means to choose a representative among them and set its label height to the sum of the individual label heights.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"296 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123462425","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 topological index is a numerical quantity that defines a chemical descriptor to report several physical, biological and chemical properties of a chemical structure. In recent literature, various degree-based topological indices of a molecular structure are easily calculated by deriving a M-polynomial of that structure. In this paper, we first determine the expression of a M-polynomial of the triangular Hex-derived network of type three of dimension n and then obtain the corresponding degree-based topological indices from the closed form of M-polynomial. In addition, we use Maple software to represent the M-polynomial and the concerned degree-based topological indices pictorially for different dimensions.
{"title":"Topological Characterization of the Third Type of Triangular Hex-derived Networks","authors":"Shibsankar Das, S. Rai","doi":"10.7561/SACS.2021.2.145","DOIUrl":"https://doi.org/10.7561/SACS.2021.2.145","url":null,"abstract":"A topological index is a numerical quantity that defines a chemical descriptor to report several physical, biological and chemical properties of a chemical structure. In recent literature, various degree-based topological indices of a molecular structure are easily calculated by deriving a M-polynomial of that structure. In this paper, we first determine the expression of a M-polynomial of the triangular Hex-derived network of type three of dimension n and then obtain the corresponding degree-based topological indices from the closed form of M-polynomial. In addition, we use Maple software to represent the M-polynomial and the concerned degree-based topological indices pictorially for different dimensions.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128247933","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 Robot Operating System (ROS) is one of the most used software framework to develop robot applications. Although it is possible to reuse packages and code from other ROS projects, ROS applications remain low level and reasoning at a higher level of abstraction is not possible. Using Model-Driven Engineering (MDE) in the context of ROS applications would allow to increase the accessibility of ROS, leverage the reusability of packages and supply validation of the software earlier in the design, using formal methods. For instance, formal verification methods would improve the overall dependability of robotic systems. Our view is that we should increase the abstraction of the systems through models using MDE methodology in order to enable the use of formal methods on ROS applications. In this paper we do a first step toward this and propose a comparative study of existing modeling alternatives aiming to help roboticists to smoothly adopt MDE. This study compares the use of modeling in ROS systems in three different ways: by means of direct UML modeling, a ROS UML profile and a ROS Domain-Specific Language. That allows us to pick the solution that better fits our needs.
{"title":"Applying MDE to ROS Systems: A Comparative Analysis","authors":"Mickaël Trezzy, I. Ober, Iulian Ober, R. Oliveira","doi":"10.7561/SACS.2021.1.111","DOIUrl":"https://doi.org/10.7561/SACS.2021.1.111","url":null,"abstract":"The Robot Operating System (ROS) is one of the most used software framework to develop robot applications. Although it is possible to reuse packages and code from other ROS projects, ROS applications remain low level and reasoning at a higher level of abstraction is not possible. Using Model-Driven Engineering (MDE) in the context of ROS applications would allow to increase the accessibility of ROS, leverage the reusability of packages and supply validation of the software earlier in the design, using formal methods. For instance, formal verification methods would improve the overall dependability of robotic systems. Our view is that we should increase the abstraction of the systems through models using MDE methodology in order to enable the use of formal methods on ROS applications. In this paper we do a first step toward this and propose a comparative study of existing modeling alternatives aiming to help roboticists to smoothly adopt MDE. This study compares the use of modeling in ROS systems in three different ways: by means of direct UML modeling, a ROS UML profile and a ROS Domain-Specific Language. That allows us to pick the solution that better fits our needs.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130343922","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 introduces an imperative process algebra based on ACP (Algebra of Communicating Processes). Like other imperative process algebras, this process algebra deals with processes of the kind that arises from the execution of imperative programs. It distinguishes itself from already existing imperative process algebras among other things by supporting abstraction from actions that are considered not to be visible. The support of abstraction of this kind opens interesting application possibilities of the process algebra. This paper goes briefly into the possibility of information-flow security analysis of the kind that is concerned with the leakage of confidential data. For the presented axiomatization, soundness and semi-completeness results with respect to a notion of branching bisimulation equivalence are established.
介绍了一种基于ACP(代数of communication Processes)的命令式进程代数。像其他命令式进程代数一样，这个进程代数处理命令式程序的执行所产生的进程。它与已经存在的命令式过程代数的区别在于，它支持从被认为不可见的操作中抽象出来。这种抽象的支持为过程代数的应用开辟了有趣的可能性。本文简要介绍了涉及机密数据泄露的信息流安全分析的可能性。对于所提出的公理化，建立了分支双模拟等价概念的完备性和半完备性结果。
{"title":"Imperative process algebra with abstraction","authors":"K. Middelburg","doi":"10.7561/SACS.2022.1.137","DOIUrl":"https://doi.org/10.7561/SACS.2022.1.137","url":null,"abstract":"This paper introduces an imperative process algebra based on ACP (Algebra of Communicating Processes). Like other imperative process algebras, this process algebra deals with processes of the kind that arises from the execution of imperative programs. It distinguishes itself from already existing imperative process algebras among other things by supporting abstraction from actions that are considered not to be visible. The support of abstraction of this kind opens interesting application possibilities of the process algebra. This paper goes briefly into the possibility of information-flow security analysis of the kind that is concerned with the leakage of confidential data. For the presented axiomatization, soundness and semi-completeness results with respect to a notion of branching bisimulation equivalence are established.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"257 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114086319","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 introduce a weighted LTL over product omega-valuation monoids that satisfy specific properties. We also introduce weighted generalized Buchi automata with epsilon-transitions, as well as weighted Buchi automata with epsilon-transitions over product omega-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Buchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Buchi automaton with epsilon-transitions. For generalized product omega-valuation monoids that satisfy specific properties we define a weighted LTL, weighted generalized Buchi automata with epsilon-transitions, and weighted Buchi automata with epsilon-transitions, and we prove the aforementioned results for generalized product omega-valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Buchi automata with epsilon-transitions is now obtained for a restricted syntactical fragment of the logic.
{"title":"A Translation of Weighted LTL Formulas to Weighted B{\" u}chi Automata over {(omega)}-valuation Monoids","authors":"Eleni Mandrali","doi":"10.7561/SACS.2021.2.223","DOIUrl":"https://doi.org/10.7561/SACS.2021.2.223","url":null,"abstract":"In this paper we introduce a weighted LTL over product omega-valuation monoids that satisfy specific properties. We also introduce weighted generalized Buchi automata with epsilon-transitions, as well as weighted Buchi automata with epsilon-transitions over product omega-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Buchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Buchi automaton with epsilon-transitions. For generalized product omega-valuation monoids that satisfy specific properties we define a weighted LTL, weighted generalized Buchi automata with epsilon-transitions, and weighted Buchi automata with epsilon-transitions, and we prove the aforementioned results for generalized product omega-valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Buchi automata with epsilon-transitions is now obtained for a restricted syntactical fragment of the logic.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127571039","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}
Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number. Sumterm splitting operators are introduced and it is argued that without further precautions the presence of these operators gives rise to instance of the so-called sum splitting paradox. A survey of solutions to the sum splitting paradox is given.
{"title":"Sumterms, Summands, Sumtuples, and Sums and the Meta-Arithmetic of Summation","authors":"J. Bergstra","doi":"10.7561/sacs.2020.2.167","DOIUrl":"https://doi.org/10.7561/sacs.2020.2.167","url":null,"abstract":"Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number. Sumterm splitting operators are introduced and it is argued that without further precautions the presence of these operators gives rise to instance of the so-called sum splitting paradox. A survey of solutions to the sum splitting paradox is given.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"205 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131909315","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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