Isabel Pita

A Maude specification of an object-oriented database model for telecommunication networks

Abstract This paper presents an object-oriented database model for broadband telecommunication networks, which can be used both for network management and for network planning purposes. The object-oriented data model has been developed using the parallel object-oriented specification language Maude [8,11], which allows us to define not only structural aspects of the database, but also procedural aspects. Several modeling approaches are compared, emphasizing the definition of the object relationships and some of the procedural aspects of the model.

A Verification Logic for Rewriting Logic

This paper proposes the development of a logic for verifying properties of programs in rewriting logic. Rewriting logic is primarily a logic of change, in which deduction corresponds directly to computation, and not a logic to talk about change in a more indirect and global manner, such as the different modal and temporal logics that can be found in the literature. We start by defining a modal action logic (VLRL) in which rewrite rules are captured as actions. The main novelty of this logic is a topological modality associated with state constructors that allows us to reason about the structure of states, stating that the current state can be decomposed into regions satisfying certain properties. Then, on top of the modal logic, we define a temporal logic for reasoning about properties of the computations generated from rewrite theories, and demonstrate its potential by means of several examples.

Towards a Verification Logic for Rewriting Logic

This paper is an initial step in the development of a logic for verifying properties of programs in rewriting logic. Rewriting logic is primarily a logic of change, in which deduction corresponds directly to computation, and not a logic to talk about change in a more indirect and global manner, such as the different modal and temporal logics that can be found in the literature.

Specification and Verification of the Tree Identify Protocol of IEEE 1394 in Rewriting Logic

Abstract. We present three descriptions, at different abstract levels, of the tree identify protocol from the IEEE 1394 serial multimedia bus standard. The descriptions are given using the language Maude based on rewriting logic. Particularly, the time aspects of the protocol are studied. We prove the correctness of the protocol in two steps. First, the descriptions are validated by an exhaustive exploration of all the possible states reachable from an initial configuration of a network, checking that always only one leader is chosen. Then, we give a formal proof showing that the desirable properties of the protocol are always fulfilled by any network, provided that the network is connected and acyclic.

Using Reflection to Specify Transaction Sequences in Rewriting Logic

We develop an application of the reflective properties of rewriting logic to the specification of the management process of broad-band telecommunications networks. The application is illustrated by a process that modifies the demand of a service between two nodes in the network. The strategy language selected for controlling the process is based on the one presented in [2] which has been enhanced with a new operation that applies a strategy over a set of objects. The specification of the system is developed in the rewriting logic language Maude, which, thanks to its reflective capabilities, can also be used for specifying internally the strategies that control the system. Several modeling approaches are compared, emphasizing the benefits obtained from using reflection to control the rewriting process as opposed to the extra effort required to control the process at the object level itself.

Proving VLRL Action Properties with the Maude Model Checker

The Verification Logic for Rewriting Logic (VLRL) is a modal action logic in which rewrite rules are captured as actions. This paper studies a possible representation of the VLRL action formulae using the Next and the Until operators of Linear Temporal Logic (LTL). In particular, it studies the use of the Maude model checker to prove VLRL action formulae. Action modalities of VLRL fix the transition that will take place in a state and the context in which it will be applied, while LTL operators do not. Thus, to represent action modalities in LTL it is necessary to transform the initial rewrite theory into a new one in which the states carry the information about the transitions used and the context in which they have taken place. VLRL properties are then studied in the transformed theory by translating VLRL formulae into equivalent LTL formulae.

A Maude specification of an object-oriented model for telecommunication networks

This paper presents an object-oriented model for broadband telecommunication networks, which can be used both for network management and for network planning purposes. The object-oriented model has been developed using the parallel object-oriented specification language Maude, which allows us to define not only structural aspects of the model but also procedural aspects. The reflective properties of rewriting logic are applied to control the rewriting process, using a strategy language that can be specified internally to the logic. Several modeling approaches are compared, emphasizing the definition of the object relationships and the benefits obtained from using reflection as opposed to the extra effort required to control the process at the object level itself.

Conditional narrowing modulo SMT and axioms

This work presents a narrowing calculus for reachability problems in order-sorted conditional rewrite theories whose underlying equational logic is composed of some theories solvable via a satisfiability modulo theories (SMT) solver plus some combination of associativity, commutativity, and identity axioms for the non-SMT part of the equational logic; the conditions of the rules can be either rewrite conditions or quantifier-free SMT formulas. For any normalized answer of a reachability problem, this calculus computes this answer, or a more general one that can be instantiated to it.

Conditional Narrowing Modulo in Rewriting Logic and Maude

This work studies the relationship between verifiable and computable answers for reachability problems in rewrite theories with an underlying membership equational logic. These problems have the form