On model checking data-independent systems with arrays without reset

A system is data-independent with respect to a data type X iff the operations it can perform on values of type X are restricted to just equality testing. The system may also store, input and output values of type X. We study model checking of systems which are data-independent with respect to two distinct type variables X and Y, and may in addition use arrays with indices from X and values from Y . Our main interest is the following parameterised model-checking problem: whether a given program satisfies a given temporal-logic formula for all non-empty nite instances of X and Y . Initially, we consider instead the abstraction where X and Y are infinite and where partial functions with finite domains are used to model arrays. Using a translation to data-independent systems without arrays, we show that the u-calculus model-checking problem is decidable for these systems. From this result, we can deduce properties of all systems with finite instances of X and Y . We show that there is a procedure for the above parameterised model-checking problem of the universal fragment of the u-calculus, such that it always terminates but may give false negatives. We also deduce that the parameterised model-checking problem of the universal disjunction-free fragment of the u-calculus is decidable. Practical motivations for model checking data-independent systems with arrays include verification of memory and cache systems, where X is the type of memory addresses, and Y the type of storable values. As an example we verify a fault-tolerant memory interface over a set of unreliable memories.Comment: Appeared in Theory and Practice of Logic Programming, vol. 4, no. 5&6, 200

Fragments of ML Decidable by Nested Data Class Memory Automata

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument

A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure

A Process Calculus for Expressing Finite Place/Transition Petri Nets

We introduce the process calculus Multi-CCS, which extends conservatively CCS with an operator of strong prefixing able to model atomic sequences of actions as well as multiparty synchronization. Multi-CCS is equipped with a labeled transition system semantics, which makes use of a minimal structural congruence. Multi-CCS is also equipped with an unsafe P/T Petri net semantics by means of a novel technique. This is the first rich process calculus, including CCS as a subcalculus, which receives a semantics in terms of unsafe, labeled P/T nets. The main result of the paper is that a class of Multi-CCS processes, called finite-net processes, is able to represent all finite (reduced) P/T nets.Comment: In Proceedings EXPRESS'10, arXiv:1011.601