In this paper we studied infinite weighted automata and a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. This counting problems are related to Dyck paths, Motzkin paths and some generalizations. These methodology uses weighted automata, equations of ordinary generating functions and continued fractions. It is a variation of the one proposed by J. Rutten.
{"title":"Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs","authors":"R. Castro, Andrés L. Ramírez, J. L. Ramírez","doi":"10.7561/SACS.2014.1.137","DOIUrl":"https://doi.org/10.7561/SACS.2014.1.137","url":null,"abstract":"In this paper we studied infinite weighted automata and a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. This counting problems are related to Dyck paths, Motzkin paths and some generalizations. These methodology uses weighted automata, equations of ordinary generating functions and continued fractions. It is a variation of the one proposed by J. Rutten.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123233653","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 an approach to non-uniform complexity in which single-pass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity class NP/poly. Moreover, we introduce a general notion of completeness for the non-uniform complexity classes of the latter kind. We also formulate a counterpart of the well-known complexity theoretic conjecture that NP is not included in P/poly. We think that the presented approach opens up an additional way of investigating issues concerning non-uniform complexity.
{"title":"Instruction Sequence Based Non-uniform Complexity Classes","authors":"J. Bergstra, K. Middelburg","doi":"10.7561/SACS.2014.1.47","DOIUrl":"https://doi.org/10.7561/SACS.2014.1.47","url":null,"abstract":"We present an approach to non-uniform complexity in which single-pass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity class NP/poly. Moreover, we introduce a general notion of completeness for the non-uniform complexity classes of the latter kind. We also formulate a counterpart of the well-known complexity theoretic conjecture that NP is not included in P/poly. We think that the presented approach opens up an additional way of investigating issues concerning non-uniform complexity.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124163759","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}
Kleene algebra with tests (KAT) is an equational system that combines Kleene and Boolean algebras. One can model basic programming constructs and assertions in KAT, which allows for its application in compiler optimization, program transformation and dataflow analysis. To provide semantics for KAT expressions, Kozen first introduced automata on guarded strings, showing that the regular sets of guarded strings plays the same role in KAT as regular languages play in Kleene algebra. Recently, Kozen described an elegant algorithm, based on “derivatives”, to construct a deterministic automaton that accepts the guarded strings denoted by a KAT expression. This algorithm generalizes Brzozowski’s algorithm for regular expressions and inherits its inefficiency arising from the explicit computation of derivatives. In the context of classical regular expressions, many efficient algorithms for compiling expressions to automata have been proposed. One of those algorithms was devised by Berry and Sethi in the 80’s (we shall refer to it as Berry-Sethi construction/algorithm, but in the literature it is also referred to as position or Glushkov automata algorithm). In this paper, we show how the Berry-Sethi algorithm can be used to compile a KAT expression to an automaton on guarded strings. Moreover, we propose a new automata model for KAT expressions and adapt the construction of Berry and Sethi to this new model.
{"title":"Position Automata for Kleene Algebra with Tests","authors":"Alexandra Silva","doi":"10.7561/SACS.2012.2.367","DOIUrl":"https://doi.org/10.7561/SACS.2012.2.367","url":null,"abstract":"Kleene algebra with tests (KAT) is an equational system that combines Kleene and Boolean algebras. One can model basic programming constructs and assertions in KAT, which allows for its application in compiler optimization, program transformation and dataflow analysis. To provide semantics for KAT expressions, Kozen first introduced automata on guarded strings, showing that the regular sets of guarded strings plays the same role in KAT as regular languages play in Kleene algebra. Recently, Kozen described an elegant algorithm, based on “derivatives”, to construct a deterministic automaton that accepts the guarded strings denoted by a KAT expression. This algorithm generalizes Brzozowski’s algorithm for regular expressions and inherits its inefficiency arising from the explicit computation of derivatives. In the context of classical regular expressions, many efficient algorithms for compiling expressions to automata have been proposed. One of those algorithms was devised by Berry and Sethi in the 80’s (we shall refer to it as Berry-Sethi construction/algorithm, but in the literature it is also referred to as position or Glushkov automata algorithm). In this paper, we show how the Berry-Sethi algorithm can be used to compile a KAT expression to an automaton on guarded strings. Moreover, we propose a new automata model for KAT expressions and adapt the construction of Berry and Sethi to this new model.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132003277","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}
htmlabstractOver the past decades, coordination languages have emerged for the specification and implementation of interaction protocols for communicating software components. This class of languages includes Reo, a platform for compositional construction of connectors. In recent years, many formalisms for describing the behavior of Reo connectors have emerged. In this paper, we give an overview of all these classes of semantic models. Furthermore, we investigate the expressiveness of two more prominent classes, constraint automata and coloring models, in detail.
{"title":"Overview of Thirty Semantic Formalisms for Reo","authors":"S. Jongmans, F. Arbab","doi":"10.7561/SACS.2012.1.201","DOIUrl":"https://doi.org/10.7561/SACS.2012.1.201","url":null,"abstract":"htmlabstractOver the past decades, coordination languages have emerged for the specification and implementation of interaction protocols for communicating software components. This class of languages includes Reo, a platform for compositional construction of connectors. In recent years, many formalisms for describing the behavior of Reo connectors have emerged. In this paper, we give an overview of all these classes of semantic models. Furthermore, we investigate the expressiveness of two more prominent classes, constraint automata and coloring models, in detail.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"21 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116857067","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}
Distributed interactions are crucial design aspects to consider in modern applications. They can be suitably designed in terms of choreographies, that are global descriptions of the coordination of several distributed parties. Global assertions define contracts for choreographies by annotating multiparty session types with logical formulae to validate the content of the exchanged messages. The introduction of such constraints is a critical design issue as it may be hard to specify contracts that allow each party to be able to progress without violating the contract. We propose three algorithms to correct inconsistent global assertions. The methods are compared by discussing their applicability and the relationships between the amended global assertions and the original (inconsistent) ones. Also, we specify a methodology that exploits our algorithms to help designers to amend their choreographies. To show how the methodology can be applied we consider a simple scenario.
{"title":"Three Algorithms and a Methodology for Amending Contracts for Choreographies","authors":"L. Bocchi, J. Lange, E. Tuosto","doi":"10.7561/SACS.2012.1.61","DOIUrl":"https://doi.org/10.7561/SACS.2012.1.61","url":null,"abstract":"Distributed interactions are crucial design aspects to consider in modern applications. They can be suitably designed in terms of choreographies, that are global descriptions of the coordination of several distributed parties. Global assertions define contracts for choreographies by annotating multiparty session types with logical formulae to validate the content of the exchanged messages. The introduction of such constraints is a critical design issue as it may be hard to specify contracts that allow each party to be able to progress without violating the contract. We propose three algorithms to correct inconsistent global assertions. The methods are compared by discussing their applicability and the relationships between the amended global assertions and the original (inconsistent) ones. Also, we specify a methodology that exploits our algorithms to help designers to amend their choreographies. To show how the methodology can be applied we consider a simple scenario.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122025288","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. Bliudze, R. Bruni, Marco Carbone, Alexandra Silva
Developing trustworthy concurrent applications is a seemingly never ending quest, which is necessary but difficult. It is necessary because mainstream systems and applications are inherently concurrent and they are pervasive to our daily life activities. It is difficult because such systems are inherently interactive and heterogeneous, so that boundaries can hardly be established for studying subsystems in isolation. Formal methods are a key instrument in resolving ambiguities and design reliable applications in a rigorous way. The authors overview major problems in the application of formal methods and outline how they are tackled by the papers collected in this volume.
{"title":"Towards Interaction Reliability in Concurrent Applications","authors":"S. Bliudze, R. Bruni, Marco Carbone, Alexandra Silva","doi":"10.7561/SACS.2012.1.1","DOIUrl":"https://doi.org/10.7561/SACS.2012.1.1","url":null,"abstract":"Developing trustworthy concurrent applications is a seemingly never ending quest, which is necessary but difficult. It is necessary because mainstream systems and applications are inherently concurrent and they are pervasive to our daily life activities. It is difficult because such systems are inherently interactive and heterogeneous, so that boundaries can hardly be established for studying subsystems in isolation. Formal methods are a key instrument in resolving ambiguities and design reliable applications in a rigorous way. The authors overview major problems in the application of formal methods and outline how they are tackled by the papers collected in this volume.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130499293","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 CO2 , a parametric calculus for contract-based computing in distributed systems. By abstracting from the actual contract language, our calculus generalises both the contracts-as-processes and contracts-as-formulae paradigms. The calculus features primitives for advertising contracts, for reaching agreements, and for querying the fulfilment of contracts. Coordination among participants happens via multi-party sessions, which are created once agreements are reached. We present two instances of our calculus, by modelling contracts as processes in a variant of CCS, and as formulae in a logic. We formally relate the two paradigms, through an encoding from contracts-as-formulae to contracts-as-processes which ensures that the promises deducible in the logical system are exactly those reachable by its encoding as a process. Finally, we present a coarse-grained taxonomy of possible misbehaviours in contract-oriented systems, and we illustrate them with the help of a variety of examples.
{"title":"Contract-Oriented Computing in CO2","authors":"Massimo Bartoletti, E. Tuosto, R. Zunino","doi":"10.7561/SACS.2012.1.5","DOIUrl":"https://doi.org/10.7561/SACS.2012.1.5","url":null,"abstract":"We present CO2 , a parametric calculus for contract-based computing in distributed systems. By abstracting from the actual contract language, our calculus generalises both the contracts-as-processes and contracts-as-formulae paradigms. The calculus features primitives for advertising contracts, for reaching agreements, and for querying the fulfilment of contracts. Coordination among participants happens via multi-party sessions, which are created once agreements are reached. We present two instances of our calculus, by modelling contracts as processes in a variant of CCS, and as formulae in a logic. We formally relate the two paradigms, through an encoding from contracts-as-formulae to contracts-as-processes which ensures that the promises deducible in the logical system are exactly those reachable by its encoding as a process. Finally, we present a coarse-grained taxonomy of possible misbehaviours in contract-oriented systems, and we illustrate them with the help of a variety of examples.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126285691","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 develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant conservation requirement for financial products proposed by Wesseling and van den Bergh by an equation in the framework developed and define a notion of financial product behaviour using this formalization. We also present some properties of financial product behaviours. The development of the framework has been influenced by previous work on the process algebra ACP.
我们开发了一个代数框架来描述和分析金融行为，即在计划时间内转移一定数量的资金的行为。在很大程度上，对金融产品的分析就是对这种行为的分析。我们将Wesseling和van den Bergh提出的金融产品的累积利息合规保护要求形式化，并使用该形式化定义了金融产品行为的概念。本文还提出了金融产品行为的一些性质。该框架的发展受到先前关于过程代数ACP的工作的影响。
{"title":"Timed Tuplix Calculus and the Wesseling and van den Bergh Equation","authors":"J. Bergstra, K. Middelburg","doi":"10.7561/SACS.2013.2.169","DOIUrl":"https://doi.org/10.7561/SACS.2013.2.169","url":null,"abstract":"We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant conservation requirement for financial products proposed by Wesseling and van den Bergh by an equation in the framework developed and define a notion of financial product behaviour using this formalization. We also present some properties of financial product behaviours. The development of the framework has been influenced by previous work on the process algebra ACP.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130106480","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}
Associate to each sequence $A$ of integers (intending to represent packet IDs) a sequence of positive integers of the same length ${mathcal M}(A)$. The $i$'th entry of ${mathcal M}(A)$ is the size (at time $i$) of the smallest buffer needed to hold out-of-order packets, where space is accounted for unreceived packets as well. Call two sequences $A$, $B$ {em equivalent} (written $Aequiv_{FB} B$) if ${mathcal M}(A)={mathcal M}(B)$. We prove the following result: any two permutations $A,B$ of the same length with $SUS(A)$, $SUS(B)leq 3$ (where SUS is the {em shuffled-up-sequences} reordering measure), and such that $Aequiv_{FB} B$ are identical. The result (which is no longer valid if we replace the upper bound 3 by 4) was motivated by RESTORED, a receiver-oriented model of network traffic we have previously introduced.
{"title":"Identifying Almost Sorted Permutations from TCP Buffer Dynamics","authors":"Gabriel Istrate","doi":"10.7561/SACS.2015.1.133","DOIUrl":"https://doi.org/10.7561/SACS.2015.1.133","url":null,"abstract":"Associate to each sequence $A$ of integers (intending to represent packet IDs) a sequence of positive integers of the same length ${mathcal M}(A)$. The $i$'th entry of ${mathcal M}(A)$ is the size (at time $i$) of the smallest buffer needed to hold out-of-order packets, where space is accounted for unreceived packets as well. Call two sequences $A$, $B$ {em equivalent} (written $Aequiv_{FB} B$) if ${mathcal M}(A)={mathcal M}(B)$. \u0000We prove the following result: any two permutations $A,B$ of the same length with $SUS(A)$, $SUS(B)leq 3$ (where SUS is the {em shuffled-up-sequences} reordering measure), and such that $Aequiv_{FB} B$ are identical. \u0000The result (which is no longer valid if we replace the upper bound 3 by 4) was motivated by RESTORED, a receiver-oriented model of network traffic we have previously introduced.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127271517","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}
Distributed algorithms have received considerable attention and were studied intensively in the past few decades. Under some hypotheses on the distributed system, there is no deterministic solution to certain classical problems. Randomised solutions are then needed to solve those problems. Probabilistic algorithms are generally simple to formulate. However, their analysis can become very complex, especially in the field of distributed computing. In this paper, we formally model in Coq a class of randomised distributed algorithms. We develop some tools to help proving impossibility results about classical problems and analysing this class of algorithms. As case studies, we examine the handshake and maximal matching problems. We show how to use our tools to formally prove properties about algorithms solving those problems.
{"title":"RDA: A Coq Library to Reason about Randomised Distributed Algorithms in the Message Passing Model","authors":"Allyx Fontaine, A. Zemmari","doi":"10.7561/SACS.2016.2.157","DOIUrl":"https://doi.org/10.7561/SACS.2016.2.157","url":null,"abstract":"Distributed algorithms have received considerable attention and were studied intensively in the past few decades. Under some hypotheses on the distributed system, there is no deterministic solution to certain classical problems. Randomised solutions are then needed to solve those problems. Probabilistic algorithms are generally simple to formulate. However, their analysis can become very complex, especially in the field of distributed computing. In this paper, we formally model in Coq a class of randomised distributed algorithms. We develop some tools to help proving impossibility results about classical problems and analysing this class of algorithms. As case studies, we examine the handshake and maximal matching problems. We show how to use our tools to formally prove properties about algorithms solving those problems.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127174249","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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