Reachability Analysis Method Research Articles

Editor’s Introduction to the Special Volume on Application of Constraints to Formal Verification

Editor’s Introduction to the Special Volume on Application of Constraints to Formal Verification

Equational Cryptographic Reasoning in the Maude-NRL Protocol Analyzer

The NRL Protocol Analyzer (NPA) is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex real-life protocols. One of the most interesting of its features is that it can be used to reason about security in face of attempted attacks on low-level algebraic properties of the functions used in a protocol. Recently, we have given for the first time a precise formal specification of the main features of the NPA inference system: its grammar-based techniques for (co-)invariant generation and its backwards narrowing reachability analysis method; both implemented in Maude as the Maude-NPA tool. This formal specification is given within the well-known rewriting framework so that the inference system is specified as a set of rewrite rules modulo an equational theory describing the behavior of the cryptographic symbols involved. This paper gives a high-level overview of the Maude-NPA tool and illustrates how it supports equational reasoning about properties of the underlying cryptographic infrastructure by means of a simple, yet nontrivial, example of an attack whose discovery essentially requires equational reasoning. It also shows how rule-based programming languages such as Maude and complex narrowing strategies are useful to model, analyze, and verify protocols.

A rewriting-based inference system for the NRL Protocol Analyzer and its meta-logical properties

The NRL Protocol Analyzer (NPA) is a tool for the formal specification and analysis of cryptographic protocols that has been used with great effect on a number of complex real-life protocols. One of the most interesting of its features is that it can be used to reason about security in face of attempted attacks on low-level algebraic properties of the functions used in a protocol. Indeed, it has been used successfully to either reproduce or discover a number of such attacks. In this paper we give for the first time a precise formal specification of the main features of the NPA inference system: its grammar-based techniques for invariant generation and its backwards reachability analysis method. This formal specification is given within the well-known rewriting framework so that the inference system is specified as a set of rewrite rules modulo an equational theory describing the behavior of the cryptographic algorithms involved. We then use this formalization to prove some important meta-logical properties about the NPA inference system, including the soundness and completeness of the search algorithm and soundness of the grammar generation algorithm. The formalization and soundness and completeness theorems not only provide also a better understanding of the NPA as it currently operates, but provide a modular basis which can be used as a starting point for increasing the types of equational theories it can handle.

Symbolic Reachability Analysis of Probabilistic Linear Hybrid Automata

We can model embedded systems as hybrid systems. Moreover, they are distributed and real-time systems. Therefore, it is important to specify and verify randomness and soft real-time properties. For the purpose of system verification, we formally define probabilistic linear hybrid automaton and its symbolic reachability analysis method. It can describe uncertainties and soft real-time characteristics.

SYMBOLIC REACHABILITY ANALYSIS FOR MULTIPLE-CLOCK SYSTEM DESIGN

This paper proposes a symbolic reachability analysis method for multiple-clock system design, which is the first approach to deal with both synchronization problems caused by metastability and rate mismatch problems caused by clock frequency mismatches in a single framework. Three methods are described to reproduce problems that occur with multiple-clock system design during reachability analysis: (1) alternate evaluation for a system with two clocks as the base-line model, (2) nondeterministic delayed evaluation to reproduce a synchronization problem, and (3) double evaluation to reproduce a clock frequency mismatch. Experimental results on ISCAS 89 benchmark show an improvement factor of average CPU time as compared to Clarke's method by 1.29, 55.41, 2.19 and 45.23 times when alternate evaluation, double evaluation, alternate evaluation with NDDE and double evaluation with NDDE is applied, respectively.

High-level Petri net for incremental analysis of object-oriented system requirements

To complement the weakness of Petri nets in terms of naturalness, modularity, and reusability, high-level Petri nets with object concepts have been suggested. It is difficult to apply these nets to the requirements specification of object-oriented software systems because of insufficient support for the object-oriented concepts. A hierarchical object-oriented Petri net (HOONet) is developed to complement the weakness of the existing formalisms and formally define its syntax and semantics. A reachability analysis method is provided to check such behavioural properties as boundedness, liveness and persistence of the HOONet models. The HOONet provides incremental modelling and analysis of the requirements with the support of object-oriented concepts.

Analysis of Hybrid Systems Based on Hybrid Net Condition/EventSystem Model

In this paper, hybrid net condition /event systems are introduced as a model for hybrid systems. The model consists of a discrete timed Petri net and a continuous Petri net which interact each other through condition and event signals. By introducing timed discrete places in the model, timing constraints in hybrid systems can be easily described. For a class of hybrid systems that can be described as linear hybrid net condition /event systems whose continuous part is a constant continuous Petri net, two methods are developed for their state reachability analysis. One is the predicate-transformation method, which is an extension of a state reachability analysis method for linear hybrid automata. The other is the path-based method, which enumerates all possible firing seqenences of discrete transitions and verifies if a given set of states can be reached from another set by firing a sequence of discrete transitions. The verification is performed by solving a constraint satisfaction problem. A technique that adds additional constraints to the problem when a discrete state is revisited along the sequence is developed and used to prevent the method from infinite enumeration. These methods provide a basis for algorithmic analysis of this class of hybrid systems.

Specification, validation, and verification of time-critical systems

In this paper, we propose a new formalism, named the Timed Communicating Finite State Machine (Timed CFSM), for specifying and verifying time-critical systems. Timed CFSM preserves the advantages of CFSM, such as the ability to express communication, synchronization and concurrency in computer systems. A given time-dependent specification can be formalized as a Timed CFSM, from which the reachability graph is constructed to verify the correctness of the specification. To cope with the space explosion problem from which all reachability analysis methods suffer, we propose a space reduction algorithm to meet the space constraint of the verification environment.

Reachability and reverse reachability analysis of CFSMs

Reachability analysis and the recently proposed reverse reachability analysis are two important verification techniques for communicating finite state machines (CFSM). The issue of the relative efficiency of reachability analysis and reverse reachability analysis is still unsettled. In this paper, we first propose a new theory of reachability and reverse reachability analysis. Based on the new theory, we discuss and analyse the suitability of these two reachability analysis methods. We then present a reachability evaluator which, given any network of CFSMs, will try to estimate the sizes of the reachable and reverse reachable state spaces by taking snapshots of the reachability and reverse reachability spaces. The core of the evaluator is the notion of random state generation with seed states, which extends the idea of random state exploration proposed in [1]. Results from example applications have shown that the evaluator provides an excellent guidance in choosing the better of the two methods.

Incremental Methods for FSM Traversal

Computing the set of reachable states of a finite state machine, is an important component of many problems in the synthesis, and formal verification of digital systems. Computing the reachable states is computationally expensive due to the explosion in the number of states in real designs. However, the process of design is usually iterative, and the designer may modify and recompute information many times. Unfortunately, the reachability computation is called each time the designer modifies the system, because current methods for reachability analysis are not incremental. The representation of the reachable states that is currently used [1] in synthesis and verification, is inherently non-updatable; in addition it tends to have a large representation, even when the finite state machine itself has a compact representation. We solve all these problems by presenting alternate ways to represent the reachable set, and incremental algorithms that can update the new representation each time the designer changes the system. The incremental algorithms use the reachable set computed at a previous iteration, and information about the changes to the system to update it, rather than compute the reachable set from the beginning. This results in considerable savings in time, as demonstrated by the results

Validating timing requirements for time basic net specifications

This article deals with the validation of formal requirement specifications of real-time systems. Formally specified requirements can be validated by both direct execution and by proving properties at the specification level. We first discuss how the timing characteristics of a system can be specified by a formalism based on high-level Petri nets. Then we show how its temporal properties can be proven by means of a symbolic execution-based proof method for time reachability analysis. Depending on the complexity of the model of the specified system, the method may contain some undecidable steps and require interaction with the user. In many practical cases, however, the method can be performed mechanically and has acceptable response times.