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Generating optimal monitors for extended regular expressions
 In Proc. of the 3rd Workshop on Runtime Verification (RV’03), volume 89 of ENTCS
, 2003
"... Ordinary software engineers and programmers can easily understand regular patterns, as shown by the immense interest in and the success of scripting languages like Perl, based essentially on regular expression pattern matching. We believe that regular expressions provide an elegant and powerful spec ..."
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Cited by 17 (7 self)
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Ordinary software engineers and programmers can easily understand regular patterns, as shown by the immense interest in and the success of scripting languages like Perl, based essentially on regular expression pattern matching. We believe that regular expressions provide an elegant and powerful specification language also for monitoring requirements, because an execution trace of a program is in fact a string of states. Extended regular expressions (EREs) add complementation to regular expressions, which brings additional benefits by allowing one to specify patterns that must not occur during an execution. Complementation gives one the power to express patterns on strings more compactly. In this paper we present a technique to generate optimal monitors from EREs. Our monitors are deterministic finite automata (DFA) and our novel contribution is to generate them using a modern coalgebraic technique called coinduction. Based on experiments with our implementation, which can be publicly tested and used over the web, we believe that our technique is more efficient than the simplistic method based on complementation of automata which can quickly lead to a highlyexponential state explosion.
Iterative circular coinduction for CoCasl in Isabelle/HOL
 FUNDAMENTAL APPROACHES TO SOFTWARE ENGINEERING, VOLUME 3442 OF LECT. NOTES COMPUT. SCI
, 2005
"... Coalgebra has in recent years been recognized as the framework of choice for the treatment of reactive systems at an appropriate level of generality. Proofs about the reactive behavior of a coalgebraic system typically rely on the method of coinduction. In comparison to ‘traditional ’ coinduction, ..."
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Cited by 6 (1 self)
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Coalgebra has in recent years been recognized as the framework of choice for the treatment of reactive systems at an appropriate level of generality. Proofs about the reactive behavior of a coalgebraic system typically rely on the method of coinduction. In comparison to ‘traditional ’ coinduction, which has the disadvantage of requiring the invention of a bisimulation relation, the method of circular coinduction allows a higher degree of automation. As part of an effort to provide proof support for the algebraiccoalgebraic specification language CoCasl, we develop a new coinductive proof strategy which iteratively constructs a bisimulation relation, thus arriving at a new variant of circular coinduction. Based on this result, we design and implement tactics for the theorem prover Isabelle which allow for both automatic and semiautomatic coinductive proofs. The flexibility of this approach is demonstrated by means of examples of (semi)automatic proofs of consequences of CoCasl specifications, automatically translated into Isabelle theories by means of the Bremen heterogeneous Casl tool set Hets.
Generating Optimal Linear Temporal Logic Monitors by Coinduction
 Proceedings of 8th Asian Computing Science Conference (ASIAN’03), volume 2896 of Lecture Notes in Computer Science
, 2004
"... A coinductionbased technique to generate an optimal monitor from a Linear Temporal Logic (LTL) formula is presented in this paper. Such a monitor receives a sequence of states (one at a time) from a running process, checks them against a requirements specification expressed as an LTL formula, a ..."
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Cited by 4 (2 self)
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A coinductionbased technique to generate an optimal monitor from a Linear Temporal Logic (LTL) formula is presented in this paper. Such a monitor receives a sequence of states (one at a time) from a running process, checks them against a requirements specification expressed as an LTL formula, and determines whether the formula has been violated or validated. It can also say whether the LTL formula is not monitorable any longer, i.e., that the formula can in the future neither be violated nor be validated. A Web interface for the presented algorithm adapted to extended regular expressions is available.
1 Automating Coinduction with Case Analysis
"... Abstract. Coinduction is a major technique employed to prove behavioral properties of systems, such as behavioral equivalence. Its automation is highly desirable, despite the fact that most behavioral problems are Π 0 2complete. Circular coinduction, which is at the core of the CIRC prover, automat ..."
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Cited by 4 (1 self)
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Abstract. Coinduction is a major technique employed to prove behavioral properties of systems, such as behavioral equivalence. Its automation is highly desirable, despite the fact that most behavioral problems are Π 0 2complete. Circular coinduction, which is at the core of the CIRC prover, automates coinduction by systematically deriving new goals and proving existing ones until, hopefully, all goals are proved. Motivated by practical examples, circular coinduction and CIRC have been recently extended with several features, such as special contexts, generalization and simplification. Unfortunately, none of these extensions eliminates the need for case analysis and, consequently, there are still many natural behavioral properties that CIRC cannot prove automatically. This paper presents an extension of circular coinduction with case analysis constructs and reasoning, as well as its implementation in CIRC. To uniformly prove the soundness of this extension, as well as of past and future extensions of circular coinduction and CIRC, this paper also proposes a general correctextension technique based on equational interpolants. 1
Dialgebraic Specification and Modeling
"... corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube ..."
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Cited by 4 (4 self)
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corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube
Behavioral institutions and refinements in generalized hidden logics
 J. Univers. Comput. Sci
, 2006
"... Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden klogics) to the algebraic specifica ..."
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Cited by 3 (3 self)
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Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden klogics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties. We reformulate the notion of hidden klogic as well as the behavioral logic of a hidden klogic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement.
Proving Equality of Streams Automatically
"... Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. In this paper we focus on equality of streams, more precisely, for a given set of equations two stream terms are said to be equal if they are equal in every model satisfyi ..."
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Cited by 1 (0 self)
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Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. In this paper we focus on equality of streams, more precisely, for a given set of equations two stream terms are said to be equal if they are equal in every model satisfying the given equations. We investigate techniques for proving equality of streams suitable for automation. Apart from techniques that were already available in the tool CIRC from Lucanu and Roşu, we also exploit welldefinedness of streams, typically proved by proving productivity. Moreover, our approach does not restrict to behavioral input format and does not require termination. We present a tool Streambox that can prove equality of a wide range of examples fully automatically. Digital Object Identifier 10.4230/LIPIcs.RTA.2011.393
Algebraic Model Checking
"... Abstract. Several more or less algebraic approaches to model checking are presented and compared with each other with respect to their range of applications and their degree of automation. All of them have been implemented and tested in our Haskellbased formalreasoning system Expander2. Besides re ..."
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Cited by 1 (1 self)
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Abstract. Several more or less algebraic approaches to model checking are presented and compared with each other with respect to their range of applications and their degree of automation. All of them have been implemented and tested in our Haskellbased formalreasoning system Expander2. Besides realizing and integrating stateofthe art proof and computation rules the system admits rarely restricted specifications of the models to be checked in terms of rewrite rules and functionallogic programs. It also offers flexible features for visualizing and even animating models and computations. Indeed, this paper does not present purely theoretical work. Due to the increasing abstraction potential of programming languages like Haskell the boundaries between developing a formal system and implementing it or making it ‘userfriendly ’ as well as between systems developed in different communities become more and more obsolete. The individual topics discussed in the paper reflect this observation. 1
London, United Kingdom
"... The structure map turning a set into the carrier of a final coalgebra is not unique. This fact is wellknown but commonly elided. In this paper we argue that any such concrete representation of a set as a final coalgebra is potentially interesting on its own. We discuss several examples, in particul ..."
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The structure map turning a set into the carrier of a final coalgebra is not unique. This fact is wellknown but commonly elided. In this paper we argue that any such concrete representation of a set as a final coalgebra is potentially interesting on its own. We discuss several examples, in particular, we consider different coalgebra structures that turn the set of infinite streams into the carrier of a final coalgebra. After that we focus on coalgebra structures that are made up using socalled cooperations. We say that a collection of cooperations is complete for a given set X if it gives rise to a coalgebra structure that turns X into the carrier set of a subcoalgebra of a final coalgebra. Any complete set of cooperations yields a coalgebraic proof and definition principle. We exploit this fact and devise a general definition scheme for constants and functions on a set X that is parametrically in the choice of the complete set of cooperations for X. Key words: Coalgebra, coinduction, infinite data structures, hidden algebra. 1