Vladimir A. Zakharov

An Approach to the Obfuscation of Control-Flow of Sequential Computer Programs

In this paper we present a straightforward approach to the obfuscation of sequential program control-flow in order to design tamperresistant software. The principal idea of our technique is as follows: Let I be an instance of a hard combinatorial problem C, whose solution K is known. Then, given a source program ?, we implant I into ? by applying semantics-preserving transformations and using K as a key. This yields as its result an obfuscated program ?I,K, such that a detection of some property P of ?I,K, which is essential for comprehending the program, gives a solution to I. Varying instances I, we obtain a family ?C of obfuscated programs such that the problem of checking P for ?C is at least as hard as C. We show how this technique works by taking for C the acceptance problem for linear bounded Turing machines, which is known to be pspace-complete.

Anti-unification algorithms and their applications in program analysis

A term t is called a template of terms t1 and t2 iff t1=tη1 and t2=tη2, for some substitutions η1 and η2. A template t of t1 and t2 is called the most specific iff for any template t′ of t1 and t2 there exists a substitution ξ such that t=t′ξ. The anti-unification problem is that of computing the most specific template of two given terms. This problem is dual to the well-known unification problem, which is the computing of the most general instance of terms. Unification is used extensively in automatic theorem proving and logic programming. We believe that anti-unification algorithms may have wide applications in program analysis. In this paper we present an efficient algorithm for computing the most specific templates of terms represented by labelled directed acyclic graphs and estimate the complexity of the anti-unification problem. We also describe techniques for invariant generation and software clone detection based on the concepts of the most specific templates and anti-unification.

An Efficient and Unified Approach to the Decidability of Equivalence of Propositional Programs

The aim of this paper is to present a unified and easy-to-use technique for deciding the equivalence problem for propositional deterministic programs. The key idea is to reduce this problem to the well-known group-theoretic problems by revealing an algebraic nature of program computations. By applying the main theorems of this paper to some traditional computational models we demonstrate that the equivalence problem for these models is decidable by the simple algorithms in polynomial time.

The Equivalence Problem for Computational Models: Decidable and Undecidable Cases

This paper presents a survey of fundamental concepts and main results in studying the equivalence problem for computer programs. We introduce some of the most-used models of computer programs, give a brief overview of the attempts to refine the boarder between decidable and undecidable cases of the equivalence problem for these models, and discuss the techniques for proving the decidability of the equivalence problem.

A formal model and verification problems for Software Defined Networks

Software Defined Networking (SDN) is an approach to building computer networks that separate and abstract data planes and control planes of these systems. In a SDN a centralized controller manages a distributed set of switches. A set of open commands for packet forwarding and flow table updating was defined in the form of a protocol known as OpenFlow. In this paper we describe an abstract formal model of SDN, introduce a tentative language for specification of SDN forwarding policies, and set up formally model-checking problems for SDNs.

An Approach to the Verification of Symmetric Parameterized Distributed Systems

Verification of computer programs is an important and difficult problem in programming. There are two main approaches to this problem—testing and formal verification. Testing assumes that a collection of sets of input data (test cases) is formed that enables one to trace all possible paths of program execution. Formal verification assumes that a formal (mathematical) model of the program is constructed and then it is proved that this model satisfies all the requirements (program specification). Since the behavior of distributed systems is usually very complicated, many errors made at the stage of distributed program development are difficult to detect using conventional testing methods. For this reason, the formal verification of programs has now become an indispensable part of the development cycle of complex distributed systems.

An invariant-based approach to the verification of asynchronous parameterized networks

A uniform verification problem for parameterized systems is to determine whether a temporal property is satisfied for every instance of the system which is composed of an arbitrary number of homogeneous processes. To cope with this problem we combine an induction-based technique for invariant generation and conventional model checking of finite state systems. At the first stage of verification we try to select automatically an appropriate invariant system. At the second stage, as soon as an invariant of the parameterized system is obtained, we verify it by means of a conventional model checking tool for temporal logics. An invariant system is one that is greater (with respect to some preorder relation) than any instance of the parameterized system. Therefore, the preorder relation involved in the invariant rule is of considerable importance. For this purpose we introduce a new type of simulation preorder - quasi-block simulation. We show that quasi-block simulation preserves the satisfiability of formulae from ACTL^@?-X and that asynchronous composition of processes is monotonic w.r.t. quasi-block simulation. This suggests the use of quasi-block simulation in the induction-based verification techniques for asynchronous networks. To demonstrate the feasibility of quasi-block simulation we implemented this technique and applied it to the verification of the Resource ReSerVation Protocol (RSVP).

On the equivalence problem for programs with mode switching

We study a formal model of imperative sequential programs and focus on the equivalence problem for some class of programs with mode switching whose runs can be divided into two stages. In the first stage a program selects an appropriate mode of computation. Several modes may be tried (switched) in turn before making the ultimate choice. Every time when the next mode is put to a test, the program brings data to some predefined state. In the second stage of the run, once a definite mode is fixed, the final result of computation is produced. We develop a new technique for simulating the behavior of such programs by means of finite automata and demonstrate that the equivalence problem for programs with mode switching is decidable within a polynomial space. By revealing a close relationships between the equivalence problem for this class of programs and the intersection emptiness problem for deterministic finite automata we show that the the former is PSPACE-complete.

On the decidability of the equivalence problem for orthogonal sequential programs

We introduce a new class OrtSP of first-order sequential programs. This class of programs is characterized by means of orthogonal substitutions θ = x1/t1, ..., xn/tn such that none of the terms ti occurs in the other terms tj, j ≠ i. We show that the equivalence problem for programs in OrtSP is decidable. We select also a subclass OrtSPout of orthogonal programs and demonstrate that the equivalence problem for programs in OrtSPout is decidable in polynomial time when the alphabet of relational symbols is finite and fixed.

On the Decidability of the Equivalence Problem for Monadic Recursive Programs

We present a uniform and easy-to-use technique for deciding the equivalence problem for deterministic monadic linear recursive programs. The key idea is to reduce this problem to the well-known group-theoretic problems by revealing an algebraic nature of program computations. We show that the equivalence problem for monadic linear recursive programs over finite and fixed alphabets of basic functions and logical conditions is decidable in polynomial time for the semantics based on the free monoids and free commutative monoids.