Efficient Hierarchical Reasoning about Functions over Numerical Domains

Sofronie-Stokkermans, Viorica

doi:10.1007/978-3-540-85845-4_17

Cited by 12 publications

(9 citation statements)

References 10 publications

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“…Besides convexity and concavity, other properties are monotonicity properties or boundedness properties. For details we refer to [28]. The equivalence of (2) and (3) in Theorem 3.1 is a locality result for the set of axioms for flows we consider: It states that the universally quantified clauses in the formula Flow q (t 0 , t 1 ), namely:…”

Section: Theorem 35mentioning

confidence: 98%

PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

2011

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This paper identifies an industrially relevant class of linear hybrid automata (LHA) called reasonable LHA for which parametric verification of convex safety properties with exhaustive entry states can be verified in polynomial time and time-bounded reachability can be decided in nondeterministic polynomial time for nonparametric verification and in exponential time for parametric verification. Properties with exhaustive entry states are restricted to runs originating in a (specified) inner envelope of some mode-invariant. Deciding whether an LHA is reasonable is shown to be decidable in polynomial time.

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Section: Theorem 35mentioning

confidence: 98%

PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

2011

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“…They have proved useful in the verification of parametrized systems [9] and properties of data structures [5,15], and in reasoning about certain properties of numerical functions [14] and functions in ordered domains [16]. Algebraic data types with size functions are shown to be decidable in [19].…”

Section: Related Workmentioning

confidence: 99%

“…is defined, and (3) for every P ∈ Pred: P M = P Theorem 1 (Completability implies extended locality [13] [14]. On the other hand, an extended theory can be extended again, so we can extend T with K 1 , then T ∪ K 1 with K 2 , and so on, if every extension satisfies (Comp w ).…”

Section: Introductionmentioning

confidence: 99%

Towards Complete Reasoning about Axiomatic Specifications

Jacobs

Kunčak

2011

Lecture Notes in Computer Science

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Abstract. To support verification of expressive properties of functional programs, we consider algebraic style specifications that may relate multiple user-defined functions, and compare multiple invocations of a function for different arguments. We present decision procedures for reasoning about such universally quantified properties of functional programs, using local theory extension methodology. We establish new classes of universally quantified formulas whose satisfiability can be checked in a complete way by finite quantifier instantiation. These classes include single-invocation axioms that generalize standard function contracts, but also certain many-invocation axioms, specifying that functions satisfy congruence, injectivity, or monotonicity with respect to abstraction functions, as well as conjunctions of some of these properties. These manyinvocation axioms can specify correctness of abstract data type implementations as well as certain information-flow properties. We also present a decidability-preserving construction that enables the same function to be specified using different classes of decidable specifications on different partitions of its domain.

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“…From this partial model, a total model can be constructed as explained in [Sof08]. This model can then be visualized as follows in Mathematica:…”

Section: Model Generation and Visualizationmentioning

confidence: 99%

System Description: H-PILoT (Version 1.9)

Ihlemann,

Sofronie-Stokkermans

2010

Preprint

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This system description provides an overview of H-PILoT (Hierarchical Proving by Instantiation in Local Theory extensions), a program for hierarchical reasoning in extensions of logical theories. H-PILoT reduces deduction problems in the theory extension to deduction problems in the base theory. Specialized provers and standard SMT solvers can be used for testing the satisfiability of the formulae obtained after the reduction. For a certain type of theory extension (namely for local theory extensions) this hierarchical reduction is sound and complete and -if the formulae obtained this way belong to a fragment decidable in the base theory -H-PILoT provides a decision procedure for testing satisfiability of ground formulae, and can also be used for model generation.

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Efficient Hierarchical Reasoning about Functions over Numerical Domains

Cited by 12 publications

References 10 publications

PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

Towards Complete Reasoning about Axiomatic Specifications

System Description: H-PILoT (Version 1.9)

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