91 research outputs found
On QBF Proofs and Preprocessing
QBFs (quantified boolean formulas), which are a superset of propositional
formulas, provide a canonical representation for PSPACE problems. To overcome
the inherent complexity of QBF, significant effort has been invested in
developing QBF solvers as well as the underlying proof systems. At the same
time, formula preprocessing is crucial for the application of QBF solvers. This
paper focuses on a missing link in currently-available technology: How to
obtain a certificate (e.g. proof) for a formula that had been preprocessed
before it was given to a solver? The paper targets a suite of commonly-used
preprocessing techniques and shows how to reconstruct certificates for them. On
the negative side, the paper discusses certain limitations of the
currently-used proof systems in the light of preprocessing. The presented
techniques were implemented and evaluated in the state-of-the-art QBF
preprocessor bloqqer.Comment: LPAR 201
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Efficient Certified Resolution Proof Checking
We present a novel propositional proof tracing format that eliminates complex
processing, thus enabling efficient (formal) proof checking. The benefits of
this format are demonstrated by implementing a proof checker in C, which
outperforms a state-of-the-art checker by two orders of magnitude. We then
formalize the theory underlying propositional proof checking in Coq, and
extract a correct-by-construction proof checker for our format from the
formalization. An empirical evaluation using 280 unsatisfiable instances from
the 2015 and 2016 SAT competitions shows that this certified checker usually
performs comparably to a state-of-the-art non-certified proof checker. Using
this format, we formally verify the recent 200 TB proof of the Boolean
Pythagorean Triples conjecture
Towards Uniform Certification in QBF
We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus, Long-Distance Q-Resolution, and Merge Resolution. These results are obtained by taking a technique of Beyersdorff et al. (JACM 2020) that turns strategy extraction into simulation and combining it with new local strategy extraction arguments.
This approach leads to simulations that are carried out mainly in propositional logic, with minimal use of the QBF rules. Our proofs therefore provide a new, largely propositional interpretation of the simulated systems. We argue that these results strengthen the case for uniform certification in QBF solving, since many QBF proof systems now fall into place underneath extended QBF Frege
Skolem Functions for Factored Formulas
Given a propositional formula F(x,y), a Skolem function for x is a function
\Psi(y), such that substituting \Psi(y) for x in F gives a formula semantically
equivalent to \exists F. Automatically generating Skolem functions is of
significant interest in several applications including certified QBF solving,
finding strategies of players in games, synthesising circuits and bit-vector
programs from specifications, disjunctive decomposition of sequential circuits
etc. In many such applications, F is given as a conjunction of factors, each of
which depends on a small subset of variables. Existing algorithms for Skolem
function generation ignore any such factored form and treat F as a monolithic
function. This presents scalability hurdles in medium to large problem
instances. In this paper, we argue that exploiting the factored form of F can
give significant performance improvements in practice when computing Skolem
functions. We present a new CEGAR style algorithm for generating Skolem
functions from factored propositional formulas. In contrast to earlier work,
our algorithm neither requires a proof of QBF satisfiability nor uses
composition of monolithic conjunctions of factors. We show experimentally that
our algorithm generates smaller Skolem functions and outperforms
state-of-the-art approaches on several large benchmarks.Comment: Full version of FMCAD 2015 conference publicatio
Verified Model Checking for Conjunctive Positive Logic
We formalize, in the Dafny language and verifier, a proof system PS for deciding the model checking problem of the fragment of first-order logic, denoted FOAE/\ , known as conjunctive positive logic (CPL). We mechanize the proofs of soundness and completeness of PS ensuring its correctness. Our formalization is representative of how various popular verification systems can be used to verify the correctness of rule-based formal systems on the basis of the least fixpoint semantics. Further, exploiting Dafny’s automatic code generation, from the completeness proof we achieve a mechanically verified prototype implementation of a proof search mechanism that is a model checker for CPL. The model checking problem of FOAE/\ is equivalent to the quantified constraint satisfaction problem (QCSP), and it is PSPACE-complete. The formalized proof system decides the general QCSP and it can be applied to arbitrary formulae of CPL.This research has been supported by the European Union (FEDER funds) under grant TIN2017-86727-C2-2-R, and by the University of the Basque Country under Project LoRea GIU18-182
Ranking function synthesis for bit-vector relations
Abstract. Ranking function synthesis is a key aspect to the success of modern termination provers for imperative programs. While it is wellknown how to generate linear ranking functions for relations over (mathematical) integers or rationals, efficient synthesis of ranking functions for machine-level integers (bit-vectors) is an open problem. This is particularly relevant for the verification of low-level code. We propose several novel algorithms to generate ranking functions for relations over machine integers: a complete method based on a reduction to Presburger arithmetic, and a template-matching approach for predefined classes of ranking functions based on reduction to SAT-and QBF-solving. The utility of our algorithms is demonstrated on examples drawn from Windows device drivers
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