Automated Synthesis of Timed and Distributed Fault-Tolerant Systems

This dissertation concentrates on the problem of automated synthesis and repair of fault-tolerant systems. In particular, given the required specification of the system, our goal is to synthesize a fault-tolerant system, or repair an existing one. We study this problem for two classes of timed and distributed systems. In the context of timed systems, we focus on efficient synthesis of fault-tolerant timed models from their fault-intolerant version. Although the complexity of the synthesis problem is known to be polynomial time in the size of the time-abstract bisimulation of the input model, the state of the art lacked synthesis algorithms that can be efficiently implemented. This is in part due to the fact that synthesis is in general a challenging problem and its complexity is significantly magnified in the context of timed systems. We propose an algorithm that takes a timed automaton, a set of fault actions, and a set of safety and bounded-time response properties as input, and utilizes a space-efficient symbolic representation of the timed automaton (called the zone graph) to synthesize a fault-tolerant timed automaton as output. The output automaton satisfies strict phased recovery, where it is guaranteed that the output model behaves similarly to the input model in the absence of faults and in the presence of faults, fault recovery is achieved in two phases, each satisfying certain safety and timing constraints. In the context of distributed systems, we study the problem of synthesizing fault-tolerant systems from their intolerant versions, when the number of processes is unknown. To synthesize a distributed fault-tolerant protocol that works for systems with any number of processes, we use counter abstraction. Using this abstraction, we deal with a finite-state abstract model to do the synthesis. Applying our proposed algorithm, we successfully synthesized a fault-tolerant distributed agreement protocol in the presence of Byzantine fault. Although the synthesis problem is known to be NP-complete in the state space of the input protocol (due to partial observability of processes) in the non-parameterized setting, our parameterized algorithm manages to synthesize a solution for a complex problem such as Byzantine agreement within less than two minutes. A system may reach a bad state due to wrong initialization or fault occurrence. One of the well-known types of distributed fault-tolerant systems are self-stabilizing systems. These are the systems that converge to their legitimate states starting from any state, and if no fault occurs, stay in legitimate states thereafter. We propose an automated sound and complete method to synthesize self-stabilizing systems starting from the desired topology and type of the system. Our proposed method is based on SMT-solving, where the desired specification of the system is formulated as SMT constraints. We used the Alloy solver to implement our method, and successfully synthesized some of the well-known self-stabilizing algorithms. We extend our method to support a type of stabilizing algorithm called ideal-stabilization, and also the case when the set of legitimate states is not explicitly known. Quantitative metrics such as recovery time are crucial in self-stabilizing systems when used in practice (such as in networking applications). One of these metrics is the average recovery time. Our automated method for synthesizing self-stabilizing systems generate some solution that respects the desired system specification, but it does not take into account any quantitative metrics. We study the problem of repairing self-stabilizing systems (where only removal of transitions is allowed) to satisfy quantitative limitations. The metric under study is average recovery time, which characterizes the performance of stabilizing programs. We show that the repair problem is NP-complete in the state space of the given system

SAVCBS 2004 Specification and Verification of Component-Based Systems: Workshop Proceedings

This is the proceedings of the 2004 SAVCBS workshop. The workshop is concerned with how formal (i.e., mathematical) techniques can be or should be used to establish a suitable foundation for the specification and verification of component-based systems. Component-based systems are a growing concern for the software engineering community. Specification and reasoning techniques are urgently needed to permit composition of systems from components. Component-based specification and verification is also vital for scaling advanced verification techniques such as extended static analysis and model checking to the size of real systems. The workshop considers formalization of both functional and non-functional behavior, such as performance or reliability

ON THE APPLICATIONS OF INTERACTIVE THEOREM PROVING IN COMPUTATIONAL SCIENCES AND ENGINEERING

Interactive Theorem Proving (ITP) is one of the most rigorous methods used in formal verification of computing systems. While ITP provides a high level of confidence in the correctness of the system under verification, it suffers from a steep learning curve and the laborious nature of interaction with a theorem prover. As such, it is desirable to investigate whether ITP can be used in unexplored (but high-impact) domains where other verification methods fail to deliver. To this end, the focus of this dissertation is on two important domains, namely design of parameterized self-stabilizing systems, and mechanical verification of numerical approximations for Riemann integration. Self-stabilization is an important property of distributed systems that enables recovery from any system configuration/state. There are important applications for self-stabilization in network protocols, game theory, socioeconomic systems, multi-agent systems and robust data structures. Most existing techniques for the design of self-stabilization rely on a ‘manual design and after-the-fact verification’ method. In a paradigm shift, we present a novel hybrid method of ‘synthesize in small scale and generalize’ where we combine the power of a finite-state synthesizer with theorem proving. We have used our method for the design of network protocols that are self-stabilizing irrespective of the number of network nodes (i.e., parameterized protocols). The second domain of application of ITP that we are investigating concentrates on formal verification of the numerical propositions of Riemann integral in formal proofs. This is a high-impact problem as Riemann Integral is considered one of the most indispensable tools of modern calculus. That has significant applications in the development of mission-critical systems in many Engineering fields that require rigorous computations such as aeronautics, space mechanics, and electrodynamics. Our contribution to this problem is three fold: first, we formally specify and verify the fundamental Riemann Integral inclusion theorem in interval arithmetic; second, we propose a general method to verify numerical propositions on Riemann Integral for a large class of integrable functions; third, we develop a set of practical automatic proof strategies based on formally verified theorems. The contributions of Part II have become part of the ultra-reliable NASA PVS standard library

Emerging trends proceedings of the 17th International Conference on Theorem Proving in Higher Order Logics: TPHOLs 2004

technical reportThis volume constitutes the proceedings of the Emerging Trends track of the 17th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2004) held September 14-17, 2004 in Park City, Utah, USA. The TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research cate- gory, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the con- ference and publication in volume 3223 of Springer?s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster session. The work-in-progress papers are held in this volume, which is published as a 2004 technical report of the School of Computing at the University of Utah