A Completion Algorithm for Lattice Tree Automata

Genet, Thomas; Gall, Tristan Le; Legay, Axel; Murat, Valérie

doi:10.1007/978-3-642-39274-0_13

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…In particular, the work presented here has strong similarities with the narrowing-based symbolic analysis of rewrite theories initiated in [48] and extended in [8]. There are also some similarities with symbolic reachability analysis based on (tree) automata (see, e.g., [32] and references there). In comparison with the tree automata methods, a considerably richer set of infinite states and properties of such states can be expressed.…”

Section: Related Work and Concluding Remarksmentioning

confidence: 75%

Rewriting modulo SMT and open system analysis

Rocha

Meseguer

Muñoz

2017

Journal of Logical and Algebraic Methods in Programming

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Abstract. This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.

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Section: Related Work and Concluding Remarksmentioning

confidence: 75%

Rewriting modulo SMT and open system analysis

Rocha

Meseguer

Muñoz

2017

Journal of Logical and Algebraic Methods in Programming

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“…These techniques rely on an extension of word automata called lattice automata. There exists a similar extension for tree automata called lattice tree automata making it possible to abstract recursive structures containing, e.g., integer values [Genet et al 2013].…”

Section: Discussionmentioning

confidence: 99%

Regular language type inference with term rewriting

Haudebourg

Genet

Jensen

2020

Proc. ACM Program. Lang.

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This paper defines a new type system applied to the fully automatic verification of safety properties of treeprocessing higher-order functional programs. We use term rewriting systems to model the program and its semantics and tree automata to model algebraic data types. We define the regular abstract interpretation of the input term rewriting system where the abstract domain is a set of regular languages. From the regular abstract interpretation we derive a type system where each type is a regular language. We define an inference procedure for this type system which allows us check the validity of safety properties. The inference mechanism is built on an invariant learning procedure based on the tree automata completion algorithm. This invariant learning procedure is regularly-complete and complete in refutation, meaning that if it is possible to give a regular type to a term then we will eventually find it, and if there is no possible type (regular or not) then we will eventually find a counterexample. CCS Concepts: • Software and its engineering → Formal software verification; Functional languages; Automated static analysis.

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“…Again, for this problem, the completion framework provides another interesting perspective. It is possible to seamlessly plug into completion any abstract domain to represent built-in subterms [48]. The structural part of the term is approximated using tree automata and the built-in part is approximated using lattices and abstract interpretation.…”

Section: Discussionmentioning

confidence: 99%

Termination criteria for tree automata completion

Genet

2016

Journal of Logical and Algebraic Methods in Programming

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This paper presents two criteria for the termination of tree automata completion. Tree automata completion is a technique for computing a tree automaton recognizing or over-approximating the set of terms reachable w.r.t. a term rewriting system. The first criterion is based on the structure of the term rewriting system itself. We prove that for most of the known classes of linear rewriting systems preserving regularity, the tree automata completion is terminating. Moreover, it outputs a tree automaton recognizing exactly the set of reachable terms. When the term rewriting system is outside of such classes, the set of reachable terms can be approximated using a set of equations defining an abstraction. The second criterion, which holds for any left-linear term rewriting system, defines sufficient restrictions on the set of equations for the tree automata completion to terminate. We then show how to take advantage of this second criterion to use completion as a new static analysis technique for functional programs. Some examples are demonstrated using the Timbuk completion tool.

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A Completion Algorithm for Lattice Tree Automata

Cited by 8 publications

References 16 publications

Rewriting modulo SMT and open system analysis

Rewriting modulo SMT and open system analysis

Regular language type inference with term rewriting

Termination criteria for tree automata completion

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