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

Intelligent search strategies based on adaptive Constraint Handling Rules

The most advanced implementation of adaptive constraint processing with Constraint Handling Rules (CHR) allows the application of intelligent search strategies to solve Constraint Satisfaction Problems (CSP). This presentation compares an improved version of conflict-directed backjumping and two variants of dynamic backtracking with respect to chronological backtracking on some of the AIM instances which are a benchmark set of random 3-SAT problems. A CHR implementation of a Boolean constraint solver combined with these different search strategies in Java is thus being compared with a CHR implementation of the same Boolean constraint solver combined with chronological backtracking in SICStus Prolog. This comparison shows that the addition of ``intelligence'' to the search process may reduce the number of search steps dramatically. Furthermore, the runtime of their Java implementations is in most cases faster than the implementations of chronological backtracking. More specifically, conflict-directed backjumping is even faster than the SICStus Prolog implementation of chronological backtracking, although our Java implementation of CHR lacks the optimisations made in the SICStus Prolog system. To appear in Theory and Practice of Logic Programming (TPLP).Comment: Number of pages: 27 Number of figures: 14 Number of Tables:

Stable Model Counting and Its Application in Probabilistic Logic Programming

Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.Comment: Accepted in AAAI, 201

A Multi-Engine Approach to Answer Set Programming

Answer Set Programming (ASP) is a truly-declarative programming paradigm proposed in the area of non-monotonic reasoning and logic programming, that has been recently employed in many applications. The development of efficient ASP systems is, thus, crucial. Having in mind the task of improving the solving methods for ASP, there are two usual ways to reach this goal: $(i)$ extending state-of-the-art techniques and ASP solvers, or $(ii)$ designing a new ASP solver from scratch. An alternative to these trends is to build on top of state-of-the-art solvers, and to apply machine learning techniques for choosing automatically the "best" available solver on a per-instance basis. In this paper we pursue this latter direction. We first define a set of cheap-to-compute syntactic features that characterize several aspects of ASP programs. Then, we apply classification methods that, given the features of the instances in a {\sl training} set and the solvers' performance on these instances, inductively learn algorithm selection strategies to be applied to a {\sl test} set. We report the results of a number of experiments considering solvers and different training and test sets of instances taken from the ones submitted to the "System Track" of the 3rd ASP Competition. Our analysis shows that, by applying machine learning techniques to ASP solving, it is possible to obtain very robust performance: our approach can solve more instances compared with any solver that entered the 3rd ASP Competition. (To appear in Theory and Practice of Logic Programming (TPLP).)Comment: 26 pages, 8 figure

Fast LTL Satisfiability Checking by SAT Solvers

Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL satisfiability checking based on bounded model checking, which does not provide a complete decision procedure, LTL satisfiability checkers have not taken advantage of the remarkable progress over the past 20 years in Boolean satisfiability solving. In this paper, we propose a new LTL satisfiability-checking framework that is accelerated using a Boolean SAT solver. Our approach is based on the variant of the \emph{obligation-set method}, which we proposed in earlier work. We describe here heuristics that allow the use of a Boolean SAT solver to analyze the obligations for a given LTL formula. The experimental evaluation indicates that the new approach provides a a significant performance advantage

Anytime Computation of Cautious Consequences in Answer Set Programming

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.Comment: To appear in Theory and Practice of Logic Programmin

SAT-Based Synthesis Methods for Safety Specs

Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their scalability limitations. Instead of BDDs, we propose several new methods to synthesize finite-state systems from safety specifications using decision procedures for the satisfiability of quantified and unquantified Boolean formulas (SAT-, QBF- and EPR-solvers). The presented approaches are based on computational learning, templates, or reduction to first-order logic. We also present an efficient parallelization, and optimizations to utilize reachability information and incremental solving. Finally, we compare all methods in an extensive case study. Our new methods outperform BDDs and other existing work on some classes of benchmarks, and our parallelization achieves a super-linear speedup. This is an extended version of [5], featuring an additional appendix.Comment: Extended version of a paper at VMCAI'1

Effectively Solving NP-SPEC Encodings by Translation to ASP

NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe Prolog and via Boolean satisfiability solvers. In this paper, we present translations from NP-SPEC into ASP, and provide an experimental evaluation of existing implementations and the proposed translations to ASP using various ASP solvers. The results show that translating to ASP clearly has an edge over the existing translation into SAT, which involves an intrinsic grounding process. We also argue that it might be useful to incorporate certain language constructs of NPSPEC into mainstream ASP