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Learning Pomset Automata [article]

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Alexandra Silva
2021 arXiv   pre-print
We extend the L* algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata.
arXiv:2102.07504v1 fatcat:lfqtrbr76vg4rp6hf333remcfi

Graph Clustering with Surprise: Complexity and Exact Solutions [article]

Tobias Fleck, Andrea Kappes, Dorothea Wagner
2013 arXiv   pre-print
Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marin proposed a related, but slightly different approach leading to the quality measure surprise, and reported good behavior in the context of synthetic and real world benchmarks. We show that the problem of finding a clustering with optimum surprise is NP-hard. Moreover, a
more » ... P-hard. Moreover, a bicriterial view on the problem permits to compute optimum solutions for small instances by solving a small number of integer linear programs, and leads to a polynomial time algorithm on trees.
arXiv:1310.6019v1 fatcat:c7d4fqv325hw3fyjbrpj3qyxfu

Decision problems for Clark-congruential languages [article]

Makoto Kanazawa, Tobias Kappé
2018 arXiv   pre-print
A common question when studying a class of context-free grammars is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical inference. We also consider the problem of checking whether a given CFG is Clark-congruential, and show that it is decidable given that the CFG is a DCFG.
arXiv:1805.04402v2 fatcat:zpykighi3jbmhctyztyvhd2pum

Learning Pomset Automata [chapter]

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Alexandra Silva
2021 Lecture Notes in Computer Science  
AbstractWe extend the $$\mathtt {L}^{\!\star }$$ L ⋆ algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata.
doi:10.1007/978-3-030-71995-1_26 fatcat:ozzr6nzrwfdczgzlztbu5bnpki

A Categorical Framework for Learning Generalised Tree Automata [article]

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, Alexandra Silva
2020 arXiv   pre-print
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify these using category theory in order to ease correctness proofs and guide the design of new algorithms. In this paper, we extend CALF to cover learning of algebraic structures that may not have a coalgebraic presentation. Furthermore, we provide a detailed
more » ... de a detailed algorithmic account of an abstract version of the popular L* algorithm, which was missing from CALF. We instantiate the abstract theory to a large class of Set functors, by which we recover for the first time practical tree automata learning algorithms from an abstract framework and at the same time obtain new algorithms to learn algebras of quotiented polynomial functors.
arXiv:2001.05786v1 fatcat:pevfelvmcjedfmcpj43na4kpva

Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness [article]

Tobias Kappé and Paul Brunet and Alexandra Silva and Jana Wagemaker and Fabio Zanasi
2020 arXiv   pre-print
Steffen Smolka, Nate Foster, Justin Hsu, Tobias Kappé, Dexter Kozen, and Alexandra Silva. Guarded Kleene algebra with tests: verification of uninterpreted programs in nearly linear time.  ...  Jana Wagemaker, Marcello Bonsangue, Tobias Kapp, Jurriaan Rot, and Alexandra Silva. Completeness and incompleteness of synchronous Kleene algebra. In MPC, 2019. doi:10.1007/978-3-030-33636-3_14.  ... 
arXiv:2002.09682v1 fatcat:uv4z53k755hd7kiubof4ijoazi

Composing Constraint Automata, State-by-State [chapter]

Sung-Shik T. Q. Jongmans, Tobias Kappé, Farhad Arbab
2016 Lecture Notes in Computer Science  
The grand composition of n automata may have a number of states/transitions exponential in n. When it does, it seems not unreasonable for the computation of that grand composition to require exponentially many resources (time, space, or both). Conversely, if the grand composition of n automata has a number of states/transitions only linear in n, we may reasonably expect the computation of that grand composition to also require only linearly many resources. Recently and problematically, we saw
more » ... matically, we saw cases of linearly-sized grand compositions whose computation required exponentially many resources. We encountered these cases in the context of Reo (a graphical language for coordinating components in component-based software), constraint automata (a general formalism for modeling systems' behavior), and our compiler for Reo based on constraint automata. Combined with earlier research on constraint automata verification, these ingredients facilitate a correctness-by-construction approach to component-based software engineering-one of the hallmarks in Sifakis' "rigorous system design". To achieve that ambitious goal, however, we need to solve the previously stated problem. In this paper we present such a solution.
doi:10.1007/978-3-319-28934-2_12 fatcat:gyfs24guxrc6blhnzu5hq7keku

Graph Clustering with Surprise: Complexity and Exact Solutions [chapter]

Tobias Fleck, Andrea Kappes, Dorothea Wagner
2014 Lecture Notes in Computer Science  
Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marín proposed a related, but slightly different approach leading to the quality measure surprise, and reported good behavior in the context of synthetic and real world benchmarks. We show that the problem of finding a clustering with optimum surprise is N Phard. Moreover, a
more » ... Phard. Moreover, a bicriterial view on the problem permits to compute optimum solutions for small instances by solving a small number of integer linear programs, and leads to a polynomial time algorithm on trees.
doi:10.1007/978-3-319-04298-5_20 fatcat:cpytwxoknzet3hhe5zmizn2ysi

Tree Automata as Algebras: Minimisation and Determinisation [article]

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, Alexandra Silva
2019 arXiv   pre-print
We study a categorical generalisation of tree automata, as Σ-algebras for a fixed endofunctor Σ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these automata. We build upon and extend an existing generalisation of the Nerode equivalence to a categorical setting, and relate it to the existence of minimal automata. Lastly, we show that generalised types of side-effects, such as non-determinism, can be captured
more » ... sm, can be captured by this framework, which leads to a general determinisation procedure.
arXiv:1904.08802v1 fatcat:viekhxtihfcn3jrujycshvroii

Partially Observable Concurrent Kleene Algebra [article]

Jana Wagemaker and Paul Brunet and Simon Docherty and Tobias Kappé and Jurriaan Rot and Alexandra Silva
2020 arXiv   pre-print
This question was studied by Jipsen [10] and later by Kappé et al. [11, 12] , who proposed Concurrent Kleene Algebra with Observations (CKAO).  ... 
arXiv:2007.07593v2 fatcat:45mi4yoyjrdv3nsc2gsbcjur4u

Soft component automata: Composition, compilation, logic, and verification

Tobias Kappé, Benjamin Lion, Farhad Arbab, Carolyn Talcott
2019 Science of Computer Programming  
The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a system that meaningfully exhibits their collective behavior. We propose an automaton-based paradigm for compositional design of such systems where an action is accompanied by one or more preferences. At run-time, these preferences provide a natural fallback mechanism for the component, while at design-time they can be used to reason about the behavior of the component in an
more » ... onent in an uncertain physical world. Using algebraic structures on preferences and actions, we can compose formal representations of individual components or agents to obtain a representation of the composed system, exhibiting intuitively meaningful behavior. We extend linear temporal logic with two unary connectives that reflect the compositional structure of actions, and show that it is decidable whether all behaviors of a given automaton satisfy a formula of this extended logic. We then show how this logic can be used to diagnose undesired behavior by tracing the falsification of a specification back to one or more culpable components. Lastly, we implement a toolchain that compiles our automata to Maude, allowing us to apply the rich model checking capability of Maude to verify agent behavior.
doi:10.1016/j.scico.2019.08.001 fatcat:w7yk633v2veovivyjsfpp6jeum

Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness [article]

Todd Schmid and Tobias Kappé and Dexter Kozen and Alexandra Silva
2021 arXiv   pre-print
URL: https://hdl.handle.net/2066/83205. 33 Steffen Smolka, Nate Foster, Justin Hsu, Tobias Kappé, Dexter Kozen, and Alexandra Silva.  ... 
arXiv:2102.08286v2 fatcat:44kcysy6tjbk5fdqpdtf4lrjfa

Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness [chapter]

Tobias Kappé, Paul Brunet, Alexandra Silva, Jana Wagemaker, Fabio Zanasi
2020 Lecture Notes in Computer Science  
Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming constructs such as conditionals and while-loops. It turns out that integrating tests in CKA is subtle, due to their interaction with parallelism. In this paper we provide a solution in the form of Concurrent Kleene Algebra with Observations (CKAO). Our main
more » ... CKAO). Our main contribution is a completeness theorem for CKAO. Our result resorts on a more general study of CKA "with hypotheses", of which CKAO turns out to be an instance: this analysis is of independent interest, as it can be applied to extensions of CKA other than CKAO. Introduction Kleene algebra with tests (KAT) is a (co)algebraic framework [17, 19] that allows one to study properties of imperative programs with conditional branching, i.e. if-statements and while-loops. KAT is build on Kleene algebra (KA) [6, 16] , the algebra of regular languages. Both KA and KAT enjoy a rich meta-theory, which makes them a suitable foundation for reasoning about program verification. In particular, it is well-known that the equational theories of KA and KAT characterise rational languages [27, 21, 16] and guarded rational languages [17] respectively. Efficient procedures for deciding equivalence have been studied in recent years, also in view of recent applications to network verification [3, 8, 28] . Concurrency is a known source of bugs and hence challenges for verification. Hoare, Struth, and collaborators [11] , have proposed an extension of KA, Concurrent Kleene Algebra (CKA), as an algebraic foundation for concurrent programming. CKA enriches the basic language of KA with a parallel composition operator · ·. Analogously to KA, CKA also has a semantic characterisation for which the equational theory is complete, in terms of rational languages of pomsets (words with a partial order on letters) [23, 24, 15] .
doi:10.1007/978-3-030-45231-5_20 fatcat:hiblehptwnh2hboxqvqyctx5qi

A Component-Oriented Framework for Autonomous Agents [chapter]

Tobias Kappé, Farhad Arbab, Carolyn Talcott
2017 Lecture Notes in Computer Science  
The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a larger system that exhibits their collective behavior in a meaningful way. We propose an automaton-based paradigm for compositional design of such systems where an action is accompanied by one or more preferences. At run-time, these preferences provide a natural fallback mechanism for the component, while at design-time they can be used to reason about the behavior of the component
more » ... or of the component in an uncertain physical world. Using structures that tell us how to compose preferences and actions, we can compose formal representations of individual components or agents to obtain a representation of the composed system. We extend Linear Temporal Logic with two unary connectives that reflect the compositional structure of the actions, and show how it can be used to diagnose undesired behavior by tracing the falsification of a specification back to one or more culpable components.
doi:10.1007/978-3-319-68034-7_2 fatcat:c4h2vbjlkja2dkn4mdjz7hdfgu

Partially Observable Concurrent Kleene Algebra

Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, Alexandra Silva, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
This question was studied by Jipsen [10] and later by Kappé et al. [11, 12] , who proposed Concurrent Kleene Algebra with Observations (CKAO).  ... 
doi:10.4230/lipics.concur.2020.20 dblp:conf/concur/WagemakerBDKR020 fatcat:b3yl27z3xjdiparebr46czphs4
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