Applications of MetiTarski in the Verification of Control and Hybrid Systems

Akbarpour, Behzad; Paulson, Lawrence C.

doi:10.1007/978-3-642-00602-9_1

Cited by 12 publications

(21 citation statements)

References 13 publications

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“…Despite significant progress over the years [38,8,20,21,9,11,39,23,40,24,25,16,12,26,41,10], the problem of invariant generation for hybrid systems remains very challenging for both non-linear discrete systems as well as for non-linear differential systems. We could cite here many tools for analysis of linear systems that resulted from improvements in static analysis and in the verification of linear hybrid systems.…”

Section: Related Work and Discussionmentioning

confidence: 99%

“…Alternatively, SAT Modulo Theory decision procedures and polynomial systems [16,17,9,18,19] could also, eventually, lead to decision procedures for invariant generation. Nonetheless, despite significant progress over the years in static analysis and formal methods for algorithms and programs verification [8,20,21,9,11,[22][23][24][25]16,12,26], the problem of invariant generation for hybrid systems remains very challenging for non-linear discrete systems as well as for non-linear differential systems with non-abstracted local and initial conditions.…”

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confidence: 98%

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Generating invariants for non-linear hybrid systems

Rebiha

Moura

Matringe

2015

Theoretical Computer Science

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We describe powerful computational techniques, relying on linear algebraic methods, for generating ideals of non-linear invariants of algebraic hybrid systems. We show that the preconditions for discrete transitions and the Lie-derivatives for continuous evolution can be viewed as morphisms, and so can be suitably represented by matrices. We reduce the non-trivial invariant generation problem to the computation of the associated eigenspaces or nullspaces by encoding the consecution requirements as specific morphisms represented by such matrices. Our methods are the first to establish very general sufficient conditions that show the existence and allow the computation of invariant ideals. Our approach also embodies a strategy to estimate certain degree bounds, leading to the discovery of rich classes of inductive invariants. By reducing the problem to related linear algebraic manipulations we are able to address various deficiencies of other state-of-the-art invariant generation methods, including the efficient treatment of non-linear hybrid systems. Our approach avoids first-order quantifier eliminations, Gröbner basis computations or direct system resolutions, thereby circumventing difficulties met by other recent techniques.

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Section: Related Work and Discussionmentioning

confidence: 99%

mentioning

confidence: 98%

Generating invariants for non-linear hybrid systems

Rebiha

Moura

Matringe

2015

Theoretical Computer Science

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“…For k ≥ 0, we say a real function f : The key result as shown by Ko [18] is that, if f (x, y) is in P C[0,1] , then max x∈ [0,1] f (x, y) is in NP C[0,1] . In general, Ko proved that:…”

Section: Complexity and Lower Boundsmentioning

confidence: 99%

Delta-Decidability over the Reals

Gao

Avigad

Clarke

2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

107

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Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any sentence A containing only bounded quantifiers and functions in F, and any positive rational number delta, decides either "A is true", or "a delta-strengthening of A is false". Moreover, if F can be computed in complexity class C, then under mild assumptions, this "delta-decision problem" for bounded Sigma k-sentences resides in Sigma k(C). The results stand in sharp contrast to the well-known undecidability of the general first-order theories with these functions, and serve as a theoretical basis for the use of numerical methods in decision procedures for formulas over the reals.Index Terms-Decision procedures, first-order theories over the reals, computable analysis.

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“…We have recently been applying MetiTarski to problems in hybrid systems and control theory [5] and to analogue circuit verification [18]. For several problems obtained from the HSolver website [42], MetiTarski performs better than HSolver [41] itself, as we describe elsewhere [5].…”

Section: Results and Related Workmentioning

confidence: 99%

MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions

2009

Self Cite

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Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which are typically rational functions derived from Taylor or continued fraction expansions. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts. MetiTarski simplifies arithmetic expressions by conversion to a recursive representation, followed by flattening of nested quotients. Applications include verifying hybrid and control systems.

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Applications of MetiTarski in the Verification of Control and Hybrid Systems

Cited by 12 publications

References 13 publications

Generating invariants for non-linear hybrid systems

Generating invariants for non-linear hybrid systems

Delta-Decidability over the Reals

MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions

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