A. Niewiadomski, P. Switalski, Teofil Sidoruk, W. Penczek
We compare the efficiency of seven modern SMT-solvers for several decision and combinatorial problems: the bounded Post correspondence problem (BPCP), the extended string correction problem (ESCP), and the Towers of Hanoi (ToH) of exponential solutions. For this purpose, we define new original reductions to SMT for all the above problems, and show their complexity. Our extensive experimental results allow for drawing quite interesting conclusions on efficiency and applicability of SMT-solvers depending on the theory used in the encoding.
{"title":"SMT-Solvers in Action: Encoding and Solving Selected Problems in NP and EXPTIME","authors":"A. Niewiadomski, P. Switalski, Teofil Sidoruk, W. Penczek","doi":"10.7561/SACS.2018.2.269","DOIUrl":"https://doi.org/10.7561/SACS.2018.2.269","url":null,"abstract":"We compare the efficiency of seven modern SMT-solvers for several decision and combinatorial problems: the bounded Post correspondence problem (BPCP), the extended string correction problem (ESCP), and the Towers of Hanoi (ToH) of exponential solutions. For this purpose, we define new original reductions to SMT for all the above problems, and show their complexity. Our extensive experimental results allow for drawing quite interesting conclusions on efficiency and applicability of SMT-solvers depending on the theory used in the encoding.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126839115","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}
Pub Date : 2018-06-25DOI: 10.1007/978-3-319-91938-6_9
E. Czeizler, Alexandru Popa, Victor-Bogdan Popescu
{"title":"Fixed Parameter Algorithms and Hardness of Approximation Results for the Structural Target Controllability Problem","authors":"E. Czeizler, Alexandru Popa, Victor-Bogdan Popescu","doi":"10.1007/978-3-319-91938-6_9","DOIUrl":"https://doi.org/10.1007/978-3-319-91938-6_9","url":null,"abstract":"","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130765253","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 reticulation of an algebra $A$ is a bounded distributive lattice ${cal L}(A)$ whose prime spectrum of filters or ideals is homeomorphic to the prime spectrum of congruences of $A$, endowed with the Stone topologies. We have obtained a construction for the reticulation of any algebra $A$ from a semi-degenerate congruence-modular variety ${cal C}$ in the case when the commutator of $A$, applied to compact congruences of $A$, produces compact congruences, in particular when ${cal C}$ has principal commutators; furthermore, it turns out that weaker conditions than the fact that $A$ belongs to a congruence-modular variety are sufficient for $A$ to have a reticulation. This construction generalizes the reticulation of a commutative unitary ring, as well as that of a residuated lattice, which in turn generalizes the reticulation of a BL-algebra and that of an MV-algebra. The purpose of constructing the reticulation for the algebras from ${cal C}$ is that of transferring algebraic and topological properties between the variety of bounded distributive lattices and ${cal C}$, and a reticulation functor is particularily useful for this transfer. We have defined and studied a reticulation functor for our construction of the reticulation in this context of universal algebra.
代数$A$的网状结构是一个有界分配格${cal L}(A)$，其滤子或理想的素谱同胚于$A$的同余的素谱，并具有Stone拓扑。我们从半退化同余模变量${cal C}$得到了任意代数$ a $的网状结构，当$ a $的对易子应用于$ a $的紧同余，产生紧同余，特别是当${cal C}$有主对易子时;进一步，证明了比$A$属于同余模变体的事实更弱的条件足以使$A$具有网状。这种构造推广了可交换酉环的网状结构，以及剩余格的网状结构，从而推广了bl -代数和mv -代数的网状结构。构造${cal C}$代数的网状结构的目的是在${cal C}$和各种有界分配格之间传递代数和拓扑性质，网状函子对于这种传递特别有用。我们定义并研究了一个网状函子，用于在通用代数的背景下构造网状。
{"title":"The Reticulation of a Universal Algebra","authors":"G. Georgescu, C. Mureşan","doi":"10.7561/SACS.2018.1.67","DOIUrl":"https://doi.org/10.7561/SACS.2018.1.67","url":null,"abstract":"The reticulation of an algebra $A$ is a bounded distributive lattice ${cal L}(A)$ whose prime spectrum of filters or ideals is homeomorphic to the prime spectrum of congruences of $A$, endowed with the Stone topologies. We have obtained a construction for the reticulation of any algebra $A$ from a semi-degenerate congruence-modular variety ${cal C}$ in the case when the commutator of $A$, applied to compact congruences of $A$, produces compact congruences, in particular when ${cal C}$ has principal commutators; furthermore, it turns out that weaker conditions than the fact that $A$ belongs to a congruence-modular variety are sufficient for $A$ to have a reticulation. This construction generalizes the reticulation of a commutative unitary ring, as well as that of a residuated lattice, which in turn generalizes the reticulation of a BL-algebra and that of an MV-algebra. The purpose of constructing the reticulation for the algebras from ${cal C}$ is that of transferring algebraic and topological properties between the variety of bounded distributive lattices and ${cal C}$, and a reticulation functor is particularily useful for this transfer. We have defined and studied a reticulation functor for our construction of the reticulation in this context of universal algebra.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126168405","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}
Bayesian inference as applied in a legal setting is about belief transfer and involves a plurality of agents and communication protocols. A forensic expert (FE) may communicate to a trier of fact (TOF) first its value of a certain likelihood ratio with respect to FE's belief state as represented by a probability function on FE's proposition space. Subsequently FE communicates its recently acquired confirmation that a certain evidence proposition is true. Then TOF performs likelihood ratio transfer mediated reasoning thereby revising their own belief state. The logical principles involved in likelihood transfer mediated reasoning are discussed in a setting where probabilistic arithmetic is done within a meadow, and with Adams conditioning placed in a central role.
{"title":"Adams Conditioning and Likelihood Ratio Transfer Mediated Inference","authors":"J. Bergstra","doi":"10.7561/SACS.2019.1.1","DOIUrl":"https://doi.org/10.7561/SACS.2019.1.1","url":null,"abstract":"Bayesian inference as applied in a legal setting is about belief transfer and involves a plurality of agents and communication protocols. \u0000A forensic expert (FE) may communicate to a trier of fact (TOF) first its value of a certain likelihood ratio with respect to FE's belief state as represented by a probability function on FE's proposition space. Subsequently FE communicates its recently acquired confirmation that a certain evidence proposition is true. Then TOF performs likelihood ratio transfer mediated reasoning thereby revising their own belief state. \u0000The logical principles involved in likelihood transfer mediated reasoning are discussed in a setting where probabilistic arithmetic is done within a meadow, and with Adams conditioning placed in a central role.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125544768","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 investigates the proof theory of multiplicative additive system virtual (MAV). MAV combines two established proof calculi: multiplicative additive linear logic (MALL) and basic system virtual (BV). Due to the presence of the self-dual non-commutative operator from BV, the calculus MAV is defined in the calculus of structures — a generalisation of the sequent calculus where inference rules can be applied in any context. A generalised cut elimination result is proven for MAV, thereby establishing the consistency of linear implication defined in the calculus. The cut elimination proof involves a termination measure based on multisets of multisets of natural numbers to handle subtle interactions between operators of BV and MAV. Proof search in MAV is proven to be a PSPACE-complete decision problem. The study of this calculus is motivated by observations about applications in computer science to the verification of protocols and to querying.
{"title":"The Consistency and Complexity of Multiplicative Additive System Virtual","authors":"Ross Horne","doi":"10.7561/SACS.2015.2.245","DOIUrl":"https://doi.org/10.7561/SACS.2015.2.245","url":null,"abstract":"This paper investigates the proof theory of multiplicative additive system virtual (MAV). MAV combines two established proof calculi: multiplicative additive linear logic (MALL) and basic system virtual (BV). Due to the presence of the self-dual non-commutative operator from BV, the calculus MAV is defined in the calculus of structures — a generalisation of the sequent calculus where inference rules can be applied in any context. A generalised cut elimination result is proven for MAV, thereby establishing the consistency of linear implication defined in the calculus. The cut elimination proof involves a termination measure based on multisets of multisets of natural numbers to handle subtle interactions between operators of BV and MAV. Proof search in MAV is proven to be a PSPACE-complete decision problem. The study of this calculus is motivated by observations about applications in computer science to the verification of protocols and to querying.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117107450","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 addresses the problem of describing and analysing internally consistent data within business process workflow specifications. We use Rodin platform for verifying the correctness of the Event-B models. These models we obtain from an ontology and an associated set of normative rules by applying mapping rules. The latter enable us to transform these specifications into Event-B modular artefacts. The resulting model, by virtue of the Event-B formalism, is very close to a typical loosely coupled component-based implementation of a business system workflow, but has the additional value of being amenable to theorem proving techniques to check and refine data representation with respect to process evolution. In this paper, we give a formal account of the design specifications defined by Event-B modules and perform verification and validation by using theorem proving techniques provided by Rodin platform.
{"title":"Verification and Validation of Formal Data-Centric Business Models","authors":"T. Umarov","doi":"10.7561/SACS.2015.2.317","DOIUrl":"https://doi.org/10.7561/SACS.2015.2.317","url":null,"abstract":"This paper addresses the problem of describing and analysing internally consistent data within business process workflow specifications. We use Rodin platform for verifying the correctness of the Event-B models. These models we obtain from an ontology and an associated set of normative rules by applying mapping rules. The latter enable us to transform these specifications into Event-B modular artefacts. The resulting model, by virtue of the Event-B formalism, is very close to a typical loosely coupled component-based implementation of a business system workflow, but has the additional value of being amenable to theorem proving techniques to check and refine data representation with respect to process evolution. In this paper, we give a formal account of the design specifications defined by Event-B modules and perform verification and validation by using theorem proving techniques provided by Rodin platform.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130048336","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 previous work carried out in the setting of program algebra, including work in the area of instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only instructions of a few of the possible kinds. In the current paper, we study instruction sequence size bounded functional completeness of all possible instruction sets for Boolean registers. We expect that the results of this study will turn out to be useful to adequately assess results of work that is concerned with lower bounds of instruction sequence size complexity.
{"title":"On Instruction Sets for Boolean Registers in Program Algebra","authors":"J. Bergstra, K. Middelburg","doi":"10.7561/SACS.2016.1.1","DOIUrl":"https://doi.org/10.7561/SACS.2016.1.1","url":null,"abstract":"In previous work carried out in the setting of program algebra, including work in the area of instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only instructions of a few of the possible kinds. In the current paper, we study instruction sequence size bounded functional completeness of all possible instruction sets for Boolean registers. We expect that the results of this study will turn out to be useful to adequately assess results of work that is concerned with lower bounds of instruction sequence size complexity.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127779198","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}
Moisil logic, having as algebraic counterpart L ukasiewicz-Moisil algebras, provide an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of L ukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the $n$-valued L ukasiewicz-Moisil algebras, in which the determination principle is also saved for arbitrary subalgebras, which are characterized by a Boolean algebra and a family of Boolean ideals. As a consequence, we prove a duality result for the $n$-valued L ukasiewicz-Moisil algebras, starting from the dual space of their Boolean center. This leads us to a duality for MV$_n$-algebras, since are equivalent to a subclass of $n$-valued L ukasiewicz-Moisil algebras.
{"title":"Mutually Exclusive Nuances of Truth in Moisil Logic","authors":"Denisa Diaconescu, I. Leustean","doi":"10.7561/SACS.2015.1.69","DOIUrl":"https://doi.org/10.7561/SACS.2015.1.69","url":null,"abstract":"Moisil logic, having as algebraic counterpart L ukasiewicz-Moisil algebras, provide an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of L ukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the $n$-valued L ukasiewicz-Moisil algebras, in which the determination principle is also saved for arbitrary subalgebras, which are characterized by a Boolean algebra and a family of Boolean ideals. As a consequence, we prove a duality result for the $n$-valued L ukasiewicz-Moisil algebras, starting from the dual space of their Boolean center. This leads us to a duality for MV$_n$-algebras, since are equivalent to a subclass of $n$-valued L ukasiewicz-Moisil algebras.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"536 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134470812","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 present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerned. The system is similar to Hoare logics, but takes into account that, by the presence of jump instructions, segments of single-pass instruction sequences may have multiple entry points and multiple exit points. It is intended to support a sound general understanding of the issues with Hoare-like logics for low-level programming languages.
{"title":"A Hoare-Like Logic of Asserted Single-Pass Instruction Sequences","authors":"J. Bergstra, K. Middelburg","doi":"10.7561/SACS.2016.2.125","DOIUrl":"https://doi.org/10.7561/SACS.2016.2.125","url":null,"abstract":"We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerned. The system is similar to Hoare logics, but takes into account that, by the presence of jump instructions, segments of single-pass instruction sequences may have multiple entry points and multiple exit points. It is intended to support a sound general understanding of the issues with Hoare-like logics for low-level programming languages.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124058909","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 Karatsuba multiplication algorithm is an algorithm for computing the product of two natural numbers represented in the binary number system. This means that the algorithm actually computes a function on bit strings. The restriction of this function to bit strings of any given length can be computed according to the Karatsuba multiplication algorithm by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We describe the instruction sequences concerned for the restrictions to bit strings of the different lengths by uniform terms from an algebraic theory.
{"title":"Instruction sequence expressions for the Karatsuba multiplication algorithm","authors":"J. Bergstra, K. Middelburg","doi":"10.7561/SACS.2018.1.39","DOIUrl":"https://doi.org/10.7561/SACS.2018.1.39","url":null,"abstract":"The Karatsuba multiplication algorithm is an algorithm for computing the product of two natural numbers represented in the binary number system. This means that the algorithm actually computes a function on bit strings. The restriction of this function to bit strings of any given length can be computed according to the Karatsuba multiplication algorithm by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We describe the instruction sequences concerned for the restrictions to bit strings of the different lengths by uniform terms from an algebraic theory.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116921170","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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