Alexei Lisitsa

Equality and Monodic First-Order temporal Logic

It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.

A SAT Attack on the Erdős Discrepancy Conjecture

In 1930s Paul Erdos conjectured that for any positive integer C in any infinite +1 -1 sequence (x_n) there exists a subsequence x_d, x_{2d}, ... , x_{kd} for some positive integers k and d, such that |x_d + x_{2d} + ... + x_{kd}|> C. The conjecture has been referred to as one of the major open problems in combinatorial number theory and discrepancy theory. For the particular case of C=1 a human proof of the conjecture exists; for C=2 a bespoke computer program had generated sequences of length 1124 having discrepancy 2, but the status of the conjecture remained open even for such a small bound. We show that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solvers, one can obtain a sequence of length 1160 with discrepancy 2 and a proof of the Erdos discrepancy conjecture for C=2, claiming that no sequence of length 1161 and discrepancy 2 exists. We also present our partial results for the case of C=3.

Temporal logic with predicate /spl lambda/-abstraction

A predicate linear temporal logic LTL/sub /spl lambda/=/ without quantifiers but with predicate /spl lambda/-abstraction mechanism and equality is considered. The models of LTL/sub /spl lambda/=/ can be naturally seen as the systems of pebbles (flexible constants) moving over the elements of some (possibly infinite) domain. This allows to use LTL/sub /spl lambda/=/ for the specification of dynamic systems using some resources, such as processes using memory locations, mobile agents occupying some sites, etc. On the other hand we show that LTL/sub /spl lambda/=/ is not recursively axiomatizable and, therefore, fully automated verification of LTL/sub /spl lambda/=/ specifications via validity checking is not, in general, possible. The result is based on computational universality of the above abstract computational model of pebble systems, which is of independent interest due to the range of possible interpretations of such systems.

Verification as a parameterized testing (experiments with the SCP4 supercompiler)

Let a program-predicate t testing another program p with respect to a given postcondition be given. Concrete tests d (data of the program p) are input data for t. Let us consider the program t when values of its argument d are unknown. Then a proof of the fact that the prediate t is true for all input data of the program p is verification of p with respect to the given postcondition. In this paper, we describe experiments on automatic verification of a number of cache coherence protocols with the SCP4 supercompiler (an optimizer of programs written in the REFAL-5 functional language).

REACHABILITY ANALYSIS IN VERIFICATION VIA SUPERCOMPILATION

We present an approach to verification of parameterized systems, which is based on program transformation technique known as supercompilation. In this approach the statements about safety properties of a system to be verified are translated into the statements about properties of the program that simulates and tests the system. Supercompilation is used then to establish the required properties of the program. In this paper we show that reachability analysis performed by supercompilation can be seen as the proof of a correctness condition by induction. We formulate suitable induction principles and proof strategies and illustrate their use by examples of verification of parameterized protocols.

Practical verification of decision-making in agent-based autonomous systems

We present a verification methodology for analysing the decision-making component in agent-based hybrid systems. Traditionally hybrid automata have been used to both implement and verify such systems, but hybrid automata based modelling, programming and verification techniques scale poorly as the complexity of discrete decision-making increases making them unattractive in situations where complex logical reasoning is required. In the programming of complex systems it has, therefore, become common to separate out logical decision-making into a separate, discrete, component. However, verification techniques have failed to keep pace with this development. We are exploring agent-based logical components and have developed a model checking technique for such components which can then be composed with a separate analysis of the continuous part of the hybrid system. Among other things this allows program model checkers to be used to verify the actual implementation of the decision-making in hybrid autonomous systems.

Computer-aided proof of Erdos discrepancy properties

In 1930s Paul Erd?s conjectured that for any positive integer C in any infinite ?1 sequence ( x n ) there exists a subsequence x d , x 2 d , x 3 d , ? , x k d , for some positive integers k and d, such that | ? i = 1 k x i ? d | C . The conjecture has been referred to as one of the major open problems in combinatorial number theory and discrepancy theory. For the particular case of C = 1 a human proof of the conjecture exists; for C = 2 a bespoke computer program had generated sequences of length 1124 of discrepancy 2, but the status of the conjecture remained open even for such a small bound. We show that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solvers, one can obtain a discrepancy 2 sequence of length 1160 and a proof of the Erd?s discrepancy conjecture for C = 2 , claiming that no discrepancy 2 sequence of length 1161, or more, exists. In the similar way, we obtain a precise bound of 127?645 on the maximal lengths of both multiplicative and completely multiplicative sequences of discrepancy 3. We also demonstrate that unrestricted discrepancy 3 sequences can be longer than 130?000.

Satellite Control Using Rational Agent Programming

Traditionally a satellite is a large and expensive piece of equipment, tightly controlled by a ground team with little scope for autonomy. The space industry has recently sought to abandon large monolithic platforms, however, in favor of multiple, smaller satellites working in teams to accomplish the task of a larger vehicle through distributed methods. Both financially and functionally motivated, such developments help reduce launch vehicle constraints and nearly eliminate ground station personnel costs, while introducing fault tolerance and redundancy into the system. Moreover, in some instances, a distributed platform is the only feasible method to accomplish a particular mission.

Declarative abstractions for agent based hybrid control systems

Modern control systems are limited in their ability to react flexibly and autonomously to changing situations by the complexity inherent in analysing environments where many variables are present. We aim to use an agent approach to help alleviate this problem and are particularly interested in the control of satellite systems using BDI agent programming as pioneered by the PRS. Such systems need to generate discrete abstractions from continuous data and then use these abstractions in rational decision making. This paper provides an architecture and interaction semantics for an abstraction engine to interact with a hybrid BDI-based control system.

Membership and Reachability Problems for Row-Monomial Transformations

In this paper we study the membership and vector reachability problems for labelled transition systems with row-monomial transformations. We show the decidability of these problems for row-monomial martix semigroups over rationals and extend these results to the wider class of matrix semigroups. After that we apply our methods to reachability problems for a class of transition systems which turn out to be equivalent to specific counter machines.