In this paper, we address complexity issues for timeline-based planning over dense temporal domains. The planning problem is modeled by means of a set of independent, but interacting, components, each one represented by a number of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). While the temporal domain is usually assumed to be discrete, here we consider the dense case. Dense timeline-based planning has been recently shown to be undecidable in the general case; decidability (NP-completeness) can be recovered by restricting to purely existential synchronization rules (trigger-less rules). In this paper, we investigate the unexplored area of intermediate cases in between these two extremes. We first show that decidability and non-primitive recursive-hardness can be proved by admitting synchronization rules with a trigger, but forcing them to suitably check constraints only in the future with respect to the trigger (future simple rules). More "tractable" results can be obtained by additionally constraining the form of intervals in future simple rules: EXPSPACE-completeness is guaranteed by avoiding singular intervals, PSPACE-completeness by admitting only intervals of the forms [0,a] and [b,$infty$[.
{"title":"Complexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground","authors":"L. Bozzelli, A. Molinari, A. Montanari, A. Peron","doi":"10.4204/EPTCS.277.14","DOIUrl":"https://doi.org/10.4204/EPTCS.277.14","url":null,"abstract":"In this paper, we address complexity issues for timeline-based planning over dense temporal domains. The planning problem is modeled by means of a set of independent, but interacting, components, each one represented by a number of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). While the temporal domain is usually assumed to be discrete, here we consider the dense case. Dense timeline-based planning has been recently shown to be undecidable in the general case; decidability (NP-completeness) can be recovered by restricting to purely existential synchronization rules (trigger-less rules). In this paper, we investigate the unexplored area of intermediate cases in between these two extremes. We first show that decidability and non-primitive recursive-hardness can be proved by admitting synchronization rules with a trigger, but forcing them to suitably check constraints only in the future with respect to the trigger (future simple rules). More \"tractable\" results can be obtained by additionally constraining the form of intervals in future simple rules: EXPSPACE-completeness is guaranteed by avoiding singular intervals, PSPACE-completeness by admitting only intervals of the forms [0,a] and [b,$infty$[.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"9 1","pages":"191-205"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88361152","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 introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been reached. The main technical result is that in games, a player can win for some values of the parameters at all, if she can win for some values below an exponential bound. For many winning conditions, this implies decidability of any statements about a player being able to win with arbitrary quantification over the parameter values. While the result seems broadly applicable, a specific motivation comes from the study of chains of strategies in games. Chains of games were recently suggested as a means to define a rationality notion based on dominance that works well with quantitative games by Bassett, Jecker, P., Raskin and Van den Boogard. From the main result of this paper, we obtain generalizations of their decidability results with much simpler proofs. As both a core technical notion in the proof of the main result, and as a notion of potential independent interest, we look at boolean functions defined via graph game forms. Graph game forms have properties akin to monotone circuits, albeit are more concise. We raise some open questions regarding how concise they are exactly, which have a flavour similar to circuit complexity. Answers to these questions could improve the bounds in the main theorem.
介绍了一种参数化有限自然数图上的自动机和对策的方法。通过允许从参数值向下计数到0并根据是否达到0进行分支来访问参数。主要的技术结果是，在游戏中，玩家可以在某些参数值下获胜，如果他可以在低于指数界限的值下获胜。对于许多获胜条件，这意味着任何关于玩家能够在参数值上任意量化获胜的陈述都是可决定的。虽然这一结果似乎具有广泛的适用性，但一个特定的动机来自于对游戏中的策略链的研究。最近，Bassett、Jecker、P.、Raskin和Van den Boogard建议将游戏链作为一种定义基于支配性的理性概念的方法，这种方法在定量游戏中非常有效。从本文的主要结果中，我们用更简单的证明得到了它们的可判性结果的推广。作为证明主要结果的核心技术概念，以及潜在的独立兴趣概念，我们来看看通过图形游戏形式定义的布尔函数。图形游戏形式具有类似于单调电路的属性，尽管更简洁。我们提出了一些关于它们到底有多简洁的开放性问题，它们有一种类似于电路复杂性的味道。这些问题的答案可以改进主要定理的范围。
{"title":"Parameterized Games and Parameterized Automata","authors":"A. Pauly","doi":"10.4204/EPTCS.277.3","DOIUrl":"https://doi.org/10.4204/EPTCS.277.3","url":null,"abstract":"We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been reached. The main technical result is that in games, a player can win for some values of the parameters at all, if she can win for some values below an exponential bound. For many winning conditions, this implies decidability of any statements about a player being able to win with arbitrary quantification over the parameter values. \u0000While the result seems broadly applicable, a specific motivation comes from the study of chains of strategies in games. Chains of games were recently suggested as a means to define a rationality notion based on dominance that works well with quantitative games by Bassett, Jecker, P., Raskin and Van den Boogard. From the main result of this paper, we obtain generalizations of their decidability results with much simpler proofs. \u0000As both a core technical notion in the proof of the main result, and as a notion of potential independent interest, we look at boolean functions defined via graph game forms. Graph game forms have properties akin to monotone circuits, albeit are more concise. We raise some open questions regarding how concise they are exactly, which have a flavour similar to circuit complexity. Answers to these questions could improve the bounds in the main theorem.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"63 1","pages":"30-42"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73335205","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}
Tobias R. Gundersen, Florian Lorber, Ulrik Nyman, Christian Ovesen
Model checking of real-time systems has evolved throughout the years. Recently, the model checker Ecdar, using timed I/O automata, was used to perform compositional verification. However, in order to fully integrate model checking of real-time systems into industrial development, we need a productive and reliable way to test if such a system conforms to its corresponding model. Hence, we present an extension of Ecdar that integrates conformance testing into a new IDE that now features modelling, verification, and testing. The new tool uses model-based mutation testing, requiring only the model and the system under test, to locate faults and to prove the absence of certain types of faults. It supports testing using either real-time or simulated time. It parallelises test-case generation and test execution to provide a significant speed-up. We also introduce new mutation operators that improve the ability to detect and locate faults. Finally, we conduct a case study with 140 faulty systems, where Ecdar detects all faults.
{"title":"Effortless Fault Localisation: Conformance Testing of Real-Time Systems in Ecdar","authors":"Tobias R. Gundersen, Florian Lorber, Ulrik Nyman, Christian Ovesen","doi":"10.4204/EPTCS.277.11","DOIUrl":"https://doi.org/10.4204/EPTCS.277.11","url":null,"abstract":"Model checking of real-time systems has evolved throughout the years. Recently, the model checker Ecdar, using timed I/O automata, was used to perform compositional verification. However, in order to fully integrate model checking of real-time systems into industrial development, we need a productive and reliable way to test if such a system conforms to its corresponding model. Hence, we present an extension of Ecdar that integrates conformance testing into a new IDE that now features modelling, verification, and testing. The new tool uses model-based mutation testing, requiring only the model and the system under test, to locate faults and to prove the absence of certain types of faults. It supports testing using either real-time or simulated time. It parallelises test-case generation and test execution to provide a significant speed-up. We also introduce new mutation operators that improve the ability to detect and locate faults. Finally, we conduct a case study with 140 faulty systems, where Ecdar detects all faults.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"40 1","pages":"147-160"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77476964","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 consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.
{"title":"On Computing the Measures of First-Order Definable Sets of Trees","authors":"Marcin Przybylko","doi":"10.4204/EPTCS.277.15","DOIUrl":"https://doi.org/10.4204/EPTCS.277.15","url":null,"abstract":"We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"8 1","pages":"206-219"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74685167","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}
P. Bouyer, Mauricio González, N. Markey, Mickael Randour
In this paper, we are interested in the synthesis of schedulers in double-weighted Markov decision processes, which satisfy both a percentile constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using a weighted reachability condition. This problem is inspired by the modelization of an electric-vehicle charging problem. We study the cartography of the problem, when one parameter varies, and show how a partial cartography can be obtained via two sequences of opimization problems. We discuss completeness and feasability of the method.
{"title":"Multi-weighted Markov Decision Processes with Reachability Objectives","authors":"P. Bouyer, Mauricio González, N. Markey, Mickael Randour","doi":"10.4204/EPTCS.277.18","DOIUrl":"https://doi.org/10.4204/EPTCS.277.18","url":null,"abstract":"In this paper, we are interested in the synthesis of schedulers in double-weighted Markov decision processes, which satisfy both a percentile constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using a weighted reachability condition. This problem is inspired by the modelization of an electric-vehicle charging problem. We study the cartography of the problem, when one parameter varies, and show how a partial cartography can be obtained via two sequences of opimization problems. We discuss completeness and feasability of the method.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"3 6 1","pages":"250-264"},"PeriodicalIF":0.0,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79889557","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 aims to apply the notions of quantum geometry and correlation to the typification of semantic relations between couples of keywords in different documents. In particular we analysed texts classified as hate / non hate speeches, containing the keywords "women", "white", and "black". The paper compares this approach to cosine similarity, a classical methodology, to cast light on the notion of "similar meaning".
{"title":"Quantum Semantic Correlations in Hate and Non-Hate Speeches","authors":"F. Galofaro, Z. Toffano, Bich-Liên Doan","doi":"10.4204/EPTCS.283.5","DOIUrl":"https://doi.org/10.4204/EPTCS.283.5","url":null,"abstract":"This paper aims to apply the notions of quantum geometry and correlation to the typification of semantic relations between couples of keywords in different documents. In particular we analysed texts classified as hate / non hate speeches, containing the keywords \"women\", \"white\", and \"black\". The paper compares this approach to cosine similarity, a classical methodology, to cast light on the notion of \"similar meaning\".","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"34 1","pages":"62-74"},"PeriodicalIF":0.0,"publicationDate":"2018-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82946468","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 combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to trace and testing semantics: the trace distributions, the trace-by-trace and the extremal probabilities approaches. In this paper, we propose novel notions of behavioral metrics that are based on the three classic approaches above, and that can be used to measure the disparities in the linear behavior of processes wrt trace and testing semantics. We study the properties of these metrics, like non-expansiveness, and we compare their expressive powers.
{"title":"Trace and Testing Metrics on Nondeterministic Probabilistic Processes","authors":"Valentina Castiglioni","doi":"10.4204/EPTCS.276.4","DOIUrl":"https://doi.org/10.4204/EPTCS.276.4","url":null,"abstract":"The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to trace and testing semantics: the trace distributions, the trace-by-trace and the extremal probabilities approaches. In this paper, we propose novel notions of behavioral metrics that are based on the three classic approaches above, and that can be used to measure the disparities in the linear behavior of processes wrt trace and testing semantics. We study the properties of these metrics, like non-expansiveness, and we compare their expressive powers.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"14 1","pages":"19-36"},"PeriodicalIF":0.0,"publicationDate":"2018-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91108907","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}
Jens Aagaard, Hans Hüttel, Mathias Jakobsen, Mikkel Kettunen
We present a binary session type system using context-free session types to a version of the applied pi-calculus of Abadi et. al. where only base terms, constants and channels can be sent. Session types resemble process terms from BPA and we use a version of bisimulation equivalence to characterize type equivalence. We present a quotiented type system defined on type equivalence classes for which type equivalence is built into the type system. Both type systems satisfy general soundness properties; this is established by an appeal to a generic session type system for psi-calculi.
{"title":"Context-Free Session Types for Applied Pi-Calculus","authors":"Jens Aagaard, Hans Hüttel, Mathias Jakobsen, Mikkel Kettunen","doi":"10.4204/EPTCS.276.3","DOIUrl":"https://doi.org/10.4204/EPTCS.276.3","url":null,"abstract":"We present a binary session type system using context-free session types to a version of the applied pi-calculus of Abadi et. al. where only base terms, constants and channels can be sent. Session types resemble process terms from BPA and we use a version of bisimulation equivalence to characterize type equivalence. We present a quotiented type system defined on type equivalence classes for which type equivalence is built into the type system. Both type systems satisfy general soundness properties; this is established by an appeal to a generic session type system for psi-calculi.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"47 1","pages":"3-18"},"PeriodicalIF":0.0,"publicationDate":"2018-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82114996","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 key to any nameless representation of syntax is how it indicates the variables we choose to use and thus, implicitly, those we discard. Standard de Bruijn representations delay discarding maximally till the leaves of terms where one is chosen from the variables in scope at the expense of the rest. Consequently, introducing new but unused variables requires term traversal. This paper introduces a nameless 'co-de-Bruijn' representation which makes the opposite canonical choice, delaying discarding minimally, as near as possible to the root. It is literate Agda: dependent types make it a practical joy to express and be driven by strong intrinsic invariants which ensure that scope is aggressively whittled down to just the support of each subterm, in which every remaining variable occurs somewhere. The construction is generic, delivering a universe of syntaxes with higher-order metavariables, for which the appropriate notion of substitution is hereditary. The implementation of simultaneous substitution exploits tight scope control to avoid busywork and shift terms without traversal. Surprisingly, it is also intrinsically terminating, by structural recursion alone.
{"title":"Everybody's Got To Be Somewhere","authors":"Conor McBride","doi":"10.4204/EPTCS.275.6","DOIUrl":"https://doi.org/10.4204/EPTCS.275.6","url":null,"abstract":"The key to any nameless representation of syntax is how it indicates the variables we choose to use and thus, implicitly, those we discard. Standard de Bruijn representations delay discarding maximally till the leaves of terms where one is chosen from the variables in scope at the expense of the rest. Consequently, introducing new but unused variables requires term traversal. This paper introduces a nameless 'co-de-Bruijn' representation which makes the opposite canonical choice, delaying discarding minimally, as near as possible to the root. It is literate Agda: dependent types make it a practical joy to express and be driven by strong intrinsic invariants which ensure that scope is aggressively whittled down to just the support of each subterm, in which every remaining variable occurs somewhere. The construction is generic, delivering a universe of syntaxes with higher-order metavariables, for which the appropriate notion of substitution is hereditary. The implementation of simultaneous substitution exploits tight scope control to avoid busywork and shift terms without traversal. Surprisingly, it is also intrinsically terminating, by structural recursion alone.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"9 1","pages":"53-69"},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88699376","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 usual reading of logical implication A → B as " if A then B " fails in intuitionistic logic: there are formulas A and B such that A → B is not provable, even though B is provable whenever A is provable. Intuitionistic rules apparently don't capture interesting meta-properties of the logic and, from a computational perspective, the programs corresponding to intuitionistic proofs are not powerful enough. Such non-provable implications are nevertheless admissible, and we study their behaviour by means of a proof term assignment and related rules of reduction. We introduce V, a calculus that is able to represent admissible inferences, while remaining in the intuitionistic world by having normal forms that are just intuitionistic terms. We then extend intuitionistic logic with principles corresponding to admissible rules. As an example, we consider the Kreisel-Putnam logic KP, for which we prove the strong normalization and the disjunction property through our term assignment. This is our first step in understanding the essence of admissible rules for intuitionistic logic.
{"title":"Admissible Tools in the Kitchen of Intuitionistic Logic","authors":"Andrea Condoluci, M. Manighetti","doi":"10.4204/EPTCS.281.2","DOIUrl":"https://doi.org/10.4204/EPTCS.281.2","url":null,"abstract":"The usual reading of logical implication A → B as \" if A then B \" fails in intuitionistic logic: there are formulas A and B such that A → B is not provable, even though B is provable whenever A is provable. Intuitionistic rules apparently don't capture interesting meta-properties of the logic and, from a computational perspective, the programs corresponding to intuitionistic proofs are not powerful enough. Such non-provable implications are nevertheless admissible, and we study their behaviour by means of a proof term assignment and related rules of reduction. We introduce V, a calculus that is able to represent admissible inferences, while remaining in the intuitionistic world by having normal forms that are just intuitionistic terms. We then extend intuitionistic logic with principles corresponding to admissible rules. As an example, we consider the Kreisel-Putnam logic KP, for which we prove the strong normalization and the disjunction property through our term assignment. This is our first step in understanding the essence of admissible rules for intuitionistic logic.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"221 1","pages":"10-23"},"PeriodicalIF":0.0,"publicationDate":"2018-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77523764","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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