117 research outputs found
Controlled and effective interpolation
Model checking is a well established technique to verify systems, exhaustively and automatically. The state space explosion, known as the main difficulty in model checking scalability, has been successfully approached by symbolic model checking which represents programs using logic, usually at the propositional or first order theories level. Craig interpolation is one of the most successful abstraction techniques used in symbolic methods. Interpolants can be efficiently generated from proofs of unsatisfiability, and have been used as means of over-approximation to generate inductive invariants, refinement predicates, and function summaries. However, interpolation is still not fully understood. For several theories it is only possible to generate one interpolant, giving the interpolation-based application no chance of further optimization via interpolation. For the theories that have interpolation systems that are able to generate different interpolants, it is not understood what makes one interpolant better than another, and how to generate the most suitable ones for a particular verification task. The goal of this thesis is to address the problems of how to generate multiple interpolants for theories that still lack this flexibility in their interpolation algorithms, and how to aim at good interpolants. This thesis extends the state-of-the-art by introducing novel interpolation frameworks for different theories. For propositional logic, this work provides a thorough theoretical analysis showing which properties are desirable in a labeling function for the Labeled Interpolation Systems framework (LIS). The Proof-Sensitive labeling function is presented, and we prove that it generates interpolants with the smallest number of Boolean connectives in the entire LIS framework. Two variants that aim at controlling the logical strength of propositional interpolants while maintaining a small size are given. The new interpolation algorithms are compared to previous ones from the literature in different model checking settings, showing that they consistently lead to a better overall verification performance. The Equalities and Uninterpreted Functions (EUF)-interpolation system, presented in this thesis, is a duality-based interpolation framework capable of generating multiple interpolants for a single proof of unsatisfiability, and provides control over the logical strength of the interpolants it generates using labeling functions. The labeling functions can be theoretically compared with respect to their strength, and we prove that two of them generate the interpolants with the smallest number of equalities. Our experiments follow the theory, showing that the generated interpolants indeed have different logical strength. We combine propositional and EUF interpolation in a model checking setting, and show that the strength of the interpolation algorithms for different theories has to be aligned in order to generate smaller interpolants. This work also introduces the Linear Real Arithmetic (LRA)-interpolation system, an interpolation framework for LRA. The framework is able to generate infinitely many interpolants of different logical strength using the duality of interpolants. The strength of the LRA interpolants can be controlled by a normalized strength factor, which makes it straightforward for an interpolationbased application to choose the level of strength it wants for the interpolants. Our experiments with the LRA-interpolation system and a model checker show that it is very important for the application to be able to fine tune the strength of the LRA interpolants in order to achieve optimal performance. The interpolation frameworks were implemented and form the interpolation module in OpenSMT2, an open source efficient SMT solver. OpenSMT2 has been integrated to the propositional interpolation-based model checkers FunFrog and eVolCheck, and to the first order interpolation-based model checkerHiFrog. This thesis presents real life model checking experiments using the novel interpolation frameworks and the tools aforementioned, showing the viability and strengths of the techniques
Conditionals and modularity in general logics
In this work in progress, we discuss independence and interpolation and
related topics for classical, modal, and non-monotonic logics
SAT-Based Methods for Circuit Synthesis
Reactive synthesis supports designers by automatically constructing correct
hardware from declarative specifications. Synthesis algorithms usually compute
a strategy, and then construct a circuit that implements it. In this work, we
study SAT- and QBF-based methods for the second step, i.e., computing circuits
from strategies. This includes methods based on QBF-certification,
interpolation, and computational learning. We present optimizations, efficient
implementations, and experimental results for synthesis from safety
specifications, where we outperform BDDs both regarding execution time and
circuit size. This is an extended version of [2], with an additional appendix.Comment: Extended version of a paper at FMCAD'1
Automated incremental software verification
Software continuously evolves to meet rapidly changing human needs. Each evolved transformation of a program is expected to preserve important correctness and security properties. Aiming to assure program correctness after a change, formal verification techniques, such as Software Model Checking, have recently benefited from fully automated solutions based on symbolic reasoning and abstraction. However, the majority of the state-of-the-art model checkers are designed that each new software version has to be verified from scratch. In this dissertation, we investigate the new Formal Incremental Verification (FIV) techniques that aim at making software analysis more efficient by reusing invested efforts between verification runs. In order to show that FIV can be built on the top of different verification techniques, we focus on three complementary approaches to automated formal verification. First, we contribute the FIV technique for SAT-based Bounded Model Checking developed to verify programs with (possibly recursive) functions with respect to the set of pre-defined assertions. We present the function-summarization framework based on Craig interpolation that allows extracting and reusing over- approximations of the function behaviors. We introduce the algorithm to revalidate the summaries of one program locally in order to prevent re-verification of another program from scratch. Second, we contribute the technique for simulation relation synthesis for loop-free programs that do not necessarily contain assertions. We introduce an SMT-based abstraction- refinement algorithm that proceeds by guessing a relation and checking whether it is a simulation relation. We present a novel algorithm for discovering simulations symbolically, by means of solving ∀∃-formulas and extracting witnessing Skolem relations. Third, we contribute the FIV technique for SMT-based Unbounded Model Checking developed to verify programs with (possibly nested) loops. We present an algorithm that automatically derives simulations between programs with different loop structures. The automatically synthesized simulation relation is then used to migrate the safe inductive invariants across the evolution boundaries. Finally, we contribute the implementation and evaluation of all our algorithmic contributions, and confirm that the state-of-the-art model checking tools can successfully be extended by the FIV capabilities
Partitioning Interpolant-Based Verificationfor effective Unbounded Model Checking
Interpolant-based model checking has been shown to be effective on large verification instances, as it efficiently combines automated abstraction and reachability fixed-point checks.
On the other hand, methods based on variable quantification have proved their ability to remove free inputs, thus projecting the search space over state variables.
In this paper we propose an integrated approach which combines the abstraction power of interpolation with techniques that rely on AIG and/or BDD representations of states, directly supporting variable quantification and fixed-point checks.
The underlying idea of this combination is to adopt AIG- or BDD-based quantifications to limit and restrict the search space and the complexity of the interpolant-based approach.
The exploited strategies, most of which are individually well-known, are integrated with a new flavor, specifically designed to improve their effectiveness on difficult verification instances.
Experimental results, specifically oriented to hard-to-solve verification problems, show the robustness of our approach
Global guidance for local generalization in model checking
SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMT-based procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for Linear Integer Arithmetic and Linear Rational Aritmetic and implement them on top of Spacer solver in Z3. Our empirical results show that GSpacer, Spacer extended with global guidance, is significantly more effective than both Spacer and sole global reasoning, and, furthermore, is insensitive to interpolation
Global Guidance for Local Generalization in Model Checking
SMT-based model checkers, especially IC3-style ones, are currently the most
effective techniques for verification of infinite state systems. They infer
global inductive invariants via local reasoning about a single step of the
transition relation of a system, while employing SMT-based procedures, such as
interpolation, to mitigate the limitations of local reasoning and allow for
better generalization. Unfortunately, these mitigations intertwine model
checking with heuristics of the underlying SMT-solver, negatively affecting
stability of model checking. In this paper, we propose to tackle the
limitations of locality in a systematic manner. We introduce explicit global
guidance into the local reasoning performed by IC3-style algorithms. To this
end, we extend the SMT-IC3 paradigm with three novel rules, designed to
mitigate fundamental sources of failure that stem from locality. We instantiate
these rules for the theory of Linear Integer Arithmetic and implement them on
top of SPACER solver in Z3. Our empirical results show that GSPACER, SPACER
extended with global guidance, is significantly more effective than both SPACER
and sole global reasoning, and, furthermore, is insensitive to interpolation.Comment: Published in CAV 202
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