Optimal Proofs for Linear Temporal Logic on Lasso Words

Basin, David; Bhatt, Bhargav; Traytel, Dmitriy

doi:10.1007/978-3-030-01090-4_3

Cited by 13 publications

(21 citation statements)

References 25 publications

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“…Related, but slightly-different, problems are addressed in [2,4,17]. The first work gives a technique to incrementally build a (partial) deductive proof from the search performed by a model checker for incomplete (partially specified) systems while proving a given LTL property holds; the second focuses on runtime monitoring, proposing a local proof system for LTL and showing how such a system can be used for the construction of online runtime monitors; the third work instead discusses a proof system to provide evidence why a trace violates an LTL specification, as opposed to certifying why the property holds on the system under verification.…”

Section: Related Work and Contributionsmentioning

confidence: 99%

“…Ternary simulation performs a symbolic simulation of the circuit using three-valued logic, in which a variable can assume also the value X (for "unknown"). The simulation starts from the state assigning to all the variables in X + , to ⊥ all those in X − (see (2)), and all the others to X. Successor states are computed by applying (3) to the current state, until a fixpoint is reached (i.e.…”

Section: Equivalence and Constant Propagationmentioning

confidence: 99%

“…Two variables x i and x j are equivalent if they are never assigned an unknown value, and they always have the same value in each state. 2 This information is then used to simplify the transition relation.…”

Section: Equivalence and Constant Propagationmentioning

confidence: 99%

“…In general, in a hardware verification context, the input system is already in this functional form. Moreover, the technique can be extended to work also in the presence of further relational constraints on both X and Y , but this is omitted here for simplicity 2. This can be easily generalised to discover also XORs, i.e.…”

mentioning

confidence: 99%

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Certifying proofs for SAT-based model checking

Griggio

Roveri

Tonetta

2021

Form Methods Syst Des

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In the context of formal verification, certifying proofs are evidences of the correctness of a model in a deduction system produced automatically as outcome of the verification. They are quite appealing for high-assurance systems because they can be verified independently by proof checkers, which are usually simpler to certify than the proof-generating tools. Model checking is one of the most prominent approaches to formal verification of temporal properties and is based on an algorithmic search of the system state space. Although modern algorithms integrate deductive methods, the generation of proofs is typically restricted to invariant properties only. Moreover, it assumes that the verification produces an inductive invariant of the original system, while model checkers usually involve a variety of complex pre-processing simplifications. In this paper we show how, exploiting the k-liveness algorithm, to extend proof generation capabilities for invariant checking to cover full linear-time temporal logic (LTL) properties, in a simple and efficient manner, with essentially no overhead for the model checker. Besides the basic k-liveness algorithm, we integrate in the proof generation a variety of widely used pre-processing techniques such as temporal decomposition, model simplification via computation of equivalences with ternary simulation, and the use of stabilizing constraints. These techniques are essential in many cases to prove that a property holds, both for invariant and for LTL model checking, and thus need to be considered within the proof. We implemented the proof generation techniques on top of IC3 engines, and show the feasibility of the approach on a variety of benchmarks taken from the literature and from the Hardware Model Checking Competition. Our results confirm that proof generation results in negligible overhead for the model checker.

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Section: Related Work and Contributionsmentioning

confidence: 99%

Section: Equivalence and Constant Propagationmentioning

confidence: 99%

Section: Equivalence and Constant Propagationmentioning

confidence: 99%

mentioning

confidence: 99%

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Certifying proofs for SAT-based model checking

Griggio

Roveri

Tonetta

2021

Form Methods Syst Des

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“…Path checking [1] is about testing whether a particular signal (or word) satisfies a given formal specification. By contrast, in model checking [2] the aim is to establish whether all outputs from a model satisfy the specification.…”

Section: Introductionmentioning

confidence: 99%

Sampling Polynomial Trajectories for LTL Verification

Selvaratnam,

Cantoni,

Davoren

et al. 2021

Preprint

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This paper concerns the verification of continuous-time polynomial spline trajectories against linear temporal logic specifications (LTL without 'next'). Each atomic proposition is assumed to represent a state space region described by a multivariate polynomial inequality. The proposed approach is based on sampling the trajectories in a manner that captures all region transitions, to yield a discrete word called a trace, which is amenable to established formal methods for path checking. The continuous-time trajectory is shown to satisfy the specification if and only if the trace does. General topological conditions on the sample points are derived that ensure a trace is recorded for arbitrary continuous paths, given arbitrary region descriptions. Using techniques from computer algebra, a trace generation algorithm is developed to satisfy these conditions when the path and region boundaries are defined by polynomials. The proposed PolyTrace algorithm has polynomial complexity in the number of atomic propositions, and is guaranteed to produce a trace of any polynomial path. Its performance is demonstrated via numerical simulations.

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A Fragment of Linear Temporal Logic for Universal Very Weak Automata

Adabala

Ehlers

2018

Lecture Notes in Computer Science

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Optimal Proofs for Linear Temporal Logic on Lasso Words

Cited by 13 publications

References 25 publications

Certifying proofs for SAT-based model checking

Certifying proofs for SAT-based model checking

Sampling Polynomial Trajectories for LTL Verification

A Fragment of Linear Temporal Logic for Universal Very Weak Automata

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