Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper,

Abstract. We illustrate the use of logic programming techniques for finite model checking of CTL formulae. We present a technique for infinite state model checking of safety properties based upon logic program specialisation and analysis techniques. The power of the approach is illustrated on several examples. For that, the efficient tools logen and ecce are used. We discuss how this approach has to be extended to handle more complicated infinite state systems and to handle arbitrary CTL formulae. 1

In recent work it has been shown that infinite state model checking can be performed by a combination of partial deduction of logic programs and abstract interpretation. This paper focuses on a particular class of problems - coverability for (infinite state) Petri nets| - and shows how existing techniques and tools for declarative programs can be successfully applied. In particular, we show that a restricted form of partial deduction is already powerful enough to decide all coverability properties of Petri Nets. We also prove that two particular instances of partial deduction exactly compute the Karp-Miller tree as well as Finkel's minimal coverability set. We thus establish a link between algorithms for Petri nets and logic program specialisation.

Abstract. In recent work it has been shown that infinite state model checking can be performed by a combination of partial deduction of logic programs and abstract interpretation. It has also been shown that partial deduction is powerful enough to mimic certain algorithms to decide coverability properties of Petri nets. These algorithms are forward algorithms and hard to scale up to deal with more complicated systems. Recently, it has been proposed to use a backward algorithm scheme instead. This scheme is applicable to so–called well–structured transition systems and was successfully used, e.g., to solve coverability problems for reset Petri nets. In this paper, we discuss how partial deduction can mimic many of these backward algorithms as well. We prove this link in particular for reset Petri nets and Petri nets with transfer and doubling arcs. We thus establish a surprising link between algorithms in Petri net theory and program specialisation, and also shed light on the power of using logic program specialisation for infinite state model checking. 1

We survey fundamental concept in inverse programming and present the Universal Resolving Algorithm (URA), an algorithm for inverse computation in a first-order, functional programming language. We discusst he principles behind the algorithm, including a three-step approach based on the notion of a perfect process tree, and demonstrate our implementation with several examples. We explaint he idea of a semantics modifier for inverse computation which allows us to perform inverse computation in other programming languages via interpreters.

Abstract. In earlier work it has been shown that finite state CTL model checking of reactive systems can be achieved by a relatively simple interpreter written in tabled logic programming. This approach is flexible in the sense that various specification formalisms can be easily targeted (e.g., Petri nets, CSP,...). Moreover, infinite state CTL model checking can be performed by analysing this interpreter using a combination of partial deduction and abstract interpretation. It has also been shown that this approach is powerful enough to decide coverability properties of various kinds of Petri nets. In this ongoing work, we are empirically evaluating these approaches on various case studies of finite, parameterised and infinite systems. For finite state systems, we show how our approach and tool compares to standard tools for finite state model checking For parameterised or infinite state model checking, we are comparing our results with, e.g., XMC, Hytech. 1

Generating inductive verification proofs for Isabelle using

Abstract. In this paper we discuss the similarities between program specialisation and inductive theorem proving, and then show how program specialisation can be used to perform inductive theorem proving. We then study this relationship in more detail for the particular problem of verifying infinite state systems in order to establish a clear link between program specialisation and inductive theorem proving. Indeed, Ecce is a program specialisation system which can be used to automatically generate abstractions for the model checking of infinite state systems. We show that to verify the abstractions generated by Ecce we may employ the proof assistant Isabelle. Thereby Ecce is used to generate the specification, hypotheses and proof script in Isabelle’s theory format. Then, in many cases, Isabelle can automatically execute these proof scripts and thereby verify the soundness of Ecce’s abstraction. In this work we focus on the specification and verification of Petri nets. 1

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. The 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.

In the paper we explain the technique of verification via supercompliation taking as an example verification of the parameterised Load Balancing Monitor system. We demonstrate detailed executable specification of the Load Balancing Monitor protocol in a functional programming language REFAL and discuss the result of its supercompilation by the supercompiler SCP4. This case study is interesting both from the point of view of verification and program specialization. From the point of view of verification, a new type of non-determinism is involved in the protocol, which has not been covered yet in previous applications of the technique. With regard to program specialization, we argued earlier that our approach to program verification may be seen as specialization of interpreters with respect to data [25]. We showed that by supercompilation of an interpreter of a simplest purely imperative programming language. The language corresponding to the Load Balancing Monitor protocol that we consider here has some features both of imperative and functional languages.