MONA: Monadic Second-Order Logic in Practice

Henriksen, Jesper G.; Jensen, Ole J.L.; Jørgensen, Michael E.; Klarlund, Nils; Paige, Robert; Rauhe, Theis; Sandholm, Anders B.

doi:10.7146/brics.v2i21.19923

Cited by 93 publications

(121 citation statements)

References 10 publications

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“…We have also built a prototype tool which encodes the proof obligations in the logic of WS1S 19 so that the system Mona [13] can be invoked. On "SCard", Mona runs out of memory after two hours of computation, having built more than 140 automata in memory.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Scalable automated proving and debugging of set-based specifications

Couchot¹,

Déharbe

Giorgetti³

et al. 2003

J. Braz. Comp. Soc.

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We present a technique to prove invariants of model-based specifications in a fragment of set theory. Proof obligations containing set theory constructs are translated to first-order logic with equality augmented with (an extension of) the theory of arrays with extensionality. The idea underlying the translation is that sets are represented by their characteristic function which, in turn, is encoded by an array of Booleans indexed on the elements of the set. A theorem proving procedure automating the verification of the proof obligations obtained by the translation is described. Furthermore, we discuss how a sub-formula can be extracted from a failed proof attempt and used by a model finder to build a counter-example. To be concrete, we use a B specification of a simple process scheduler on which we illustrate our technique.

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Section: Resultsmentioning

confidence: 99%

“…The reader with some knowledge of WS1S [6] may wonder whether SSET can be translated to such a logic so that proof obligations can be discharged by existing tools such as, for example, Mona [13]. The answer to this question is indeed positive.…”

Section: Relationships With Ws1smentioning

confidence: 99%

Scalable automated proving and debugging of set-based specifications

Couchot¹,

Déharbe

Giorgetti³

et al. 2003

J. Braz. Comp. Soc.

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show abstract

“…The downside of this approach is that existing algorithms are main-memory intensive. Furthermore, the implemented system is typically applicable to only a limited probabilistic model (e.g., [44] supports just ProTDB documents, though it should be possible to use a similar bottom-up approach for hierarchical Markov chains [10] and to support continuous distributions [7]), and to a limited class of queries (e.g., [44] supports just tree patterns, but it should also be possible to extend it to MSO by combining the algorithm of [20] and a toolkit such as Mona [30] for converting queries into tree automata).…”

Section: Independent Implementationmentioning

confidence: 99%

Probabilistic XML: Models and Complexity

Kimelfeld

Senellart

2013

Advances in Probabilistic Databases for Uncertain Information Management

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Abstract. Uncertainty in data naturally arises in various applications, such as data integration and Web information extraction. Probabilistic XML is one of the concepts that have been proposed to model and manage various kinds of uncertain data. In essence, a probabilistic XML document is a compact representation of a probability distribution over ordinary XML documents. Various models of probabilistic XML provide different languages, with various degrees of expressiveness, for such compact representations. Beyond representation, probabilistic XML systems are expected to support data management in a way that properly reflects the uncertainty. For instance, query evaluation entails probabilistic inference, and update operations need to properly change the entire probability space. Efficiently and effectively accomplishing data-management tasks in that manner is a major technical challenge. This chapter reviews the literature on probabilistic XML. Specifically, this chapter discusses the probabilistic XML models that have been proposed, and the complexity of query evaluation therein. Also discussed are other data-management tasks like updates and compression, as well as systemic and implementation aspects.

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“…The MONA tool [8] is a successful implementation of wMSO. An analysis by the MONA team is used as hint for what might contribute to efficiency [10].…”

Section: Related Workmentioning

confidence: 99%

“…The most mature implementation of any variant of MSO is MONA [8], an implementation of the decision procedure for weak MSO over words and trees (wMSO, also WS1S and WS2S), a variant of MSO deciable by the use of finite automata. In MONA, minimization in every step is crucial for the efficiency [10], We use this insight to handle MSO over ω-words efficiently.…”

Section: Introductionmentioning

confidence: 99%

Deciding Monadic Second Order Logic over $$\omega $$ ω -Words by Specialized Finite Automata

Barth

2016

Lecture Notes in Computer Science

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Abstract. Several automata models are each capable of describing all ω-regular languages. The most well-known such models are Büchi, parity, Rabin, Streett, and Muller automata. We present deeper insights and further enhancements to a lesser-known model. This model was chosen and the enhancements developed with a specific goal: Decide monadic second order logic (MSO) over infinite words more efficiently.MSO over various structures is of interest in different applications, mostly in formal verification. Due to its inherent high complexity, most solvers are designed to work only for subsets of MSO. The most notable full implementation of the decision procedure is MONA, which decides MSO formulae over finite words and trees.To obtain a suitable automaton model, we further studied a representation of ω-regular languages by regular languages, which we call loop automata. We developed an efficient algorithm for homomorphisms in this representation, which is essential for deciding MSO. Aside from the algorithm for homomorphism, all algorithms for deciding MSO with loop automata are simple. Minimization of loop automata is basically the same as minimization of deterministic finite automata. Efficient minimization is an important feature for an efficient decision procedure for MSO. Together this should theoretically make loop automata a wellsuited model for efficiently deciding MSO over ω-words.Our experimental evaluation suggests that loop automata are indeed well suited for deciding MSO over ω-words efficiently.

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MONA: Monadic Second-Order Logic in Practice

Cited by 93 publications

References 10 publications

Scalable automated proving and debugging of set-based specifications

Scalable automated proving and debugging of set-based specifications

Probabilistic XML: Models and Complexity

Deciding Monadic Second Order Logic over $$\omega $$ ω -Words by Specialized Finite Automata

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