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

A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem

The Task Graph Cost-Optimal Scheduling Problem consists in scheduling a certain number of interdependent tasks onto a set of heterogeneous processors (characterized by idle and running rates per time unit), minimizing the cost of the entire process. This paper provides a novel formulation for this scheduling puzzle, in which an optimal solution is computed through a sequence of Binate Covering Problems, hinged within a Bounded Model Checking paradigm. In this approach, each covering instance, providing a min-cost trace for a given schedule depth, can be solved with several strategies, resorting to Minimum-Cost Satisfiability solvers or Pseudo-Boolean Optimization tools. Unfortunately, all direct resolution methods show very low efficiency and scalability. As a consequence, we introduce a specialized method to solve the same sequence of problems, based on a traditional all-solution SAT solver. This approach follows the "circuit cofactoring" strategy, as it exploits a powerful technique to capture a large set of solutions for any new SAT counter-example. The overall method is completed with a branch-and-bound heuristic which evaluates lower and upper bounds of the schedule length, to reduce the state space that has to be visited. Our results show that the proposed strategy significantly improves the blind binate covering schema, and it outperforms general purpose state-of-the-art tool

Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete

Reformulation in planning

Reformulation of a problem is intended to make the problem more amenable to efficient solution. This is equally true in the special case of reformulating a planning problem. This paper considers various ways in which reformulation can be exploited in planning

Special section on advances in reachability analysis and decision procedures: contributions to abstraction-based system verification

Reachability analysis asks whether a system can evolve from legitimate initial states to unsafe states. It is thus a fundamental tool in the validation of computational systems - be they software, hardware, or a combination thereof. We recall a standard approach for reachability analysis, which captures the system in a transition system, forms another transition system as an over-approximation, and performs an incremental fixed-point computation on that over-approximation to determine whether unsafe states can be reached. We show this method to be sound for proving the absence of errors, and discuss its limitations for proving the presence of errors, as well as some means of addressing this limitation. We then sketch how program annotations for data integrity constraints and interface specifications - as in Bertrand Meyers paradigm of Design by Contract - can facilitate the validation of modular programs, e.g., by obtaining more precise verification conditions for software verification supported by automated theorem proving. Then we recap how the decision problem of satisfiability for formulae of logics with theories - e.g., bit-vector arithmetic - can be used to construct an over-approximating transition system for a program. Programs with data types comprised of bit-vectors of finite width require bespoke decision procedures for satisfiability. Finite-width data types challenge the reduction of that decision problem to one that off-the-shelf tools can solve effectively, e.g., SAT solvers for propositional logic. In that context, we recall the Tseitin encoding which converts formulae from that logic into conjunctive normal form - the standard format for most SAT solvers - with only linear blow-up in the size of the formula, but linear increase in the number of variables. Finally, we discuss the contributions that the three papers in this special section make in the areas that we sketched above. © Springer-Verlag 2009

Bounded LTL Model Checking with Stable Models

In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a requirement on the behaviour of the net can be translated into a logic program such that the bounded model checking problem for the net can be solved by computing stable models of the corresponding program. The use of the stable model semantics leads to compact encodings of bounded reachability and deadlock detection tasks as well as the more general problem of bounded model checking of linear temporal logic. Correctness proofs of the devised translations are given, and some experimental results using the translation and the Smodels system are presented.Comment: 32 pages, to appear in Theory and Practice of Logic Programmin