Multiset Rewriting Research Articles

A formal model of concurrent systems based on bipartite directed acyclic graph

This paper presents a formal model of concurrent systems to represent scopes of communication channel names precisely. The model presented here is an extension of a multiset rewriting system. A bipartite directed acyclic graph represents a concurrent system consisting of a number of processes and messages. Each process or message corresponds to a source node of the graph. Names used for communication channel in the system are sink nodes. The edges of the graph represent the scopes of the names in the system. The operational semantics of the system is given as a labeled transition system. The model presented here makes it possible to represent local names that their scope are not nested. We define an equivalence relation that two systems are equivalent not only in their behavior but extrusions of scopes of names.

COMPLEXITY OF BIO-COMPUTATION: SYMBOLIC DYNAMICS IN MEMBRANE SYSTEMS

We discuss aspects of biological relevance to the modelling of bio-computation in a multiset rewriting system context: turnover, robustness against perturbations, and the dataflow programming paradigm. The systems under consideration are maximally parallel and asynchronous parallel membrane systems, the latter corresponding to computation in which the notion of time is operationally meaningless. A natural geometrical setting which seems promising for the study of computational processes in general multiset rewriting systems is presented. Configuration space corresponds to a subset of the lattice [Formula: see text], d ∈ N, and state transitions correspond to vector addition. The similarities and differences with Vector Addition Systems and Petri nets are discussed. Symbolic dynamics are introduced on special partitions of configuration space and we indicate different notions of complexity for membrane systems based on this and related concepts such as graph complexity and minimal automata. Some examples of synchronized, pipelined dataflow computations are given and decompositions into functional subunits are briefly commented on.

Polymorphic Systems with Arrays, 2-Counter Machines and Multiset Rewriting

Polymorphic systems with arrays (PSAs) is a general class of nondeterministic reactive systems. A PSA is polymorphic in the sense that it depends on a signature, which consists of a number of type variables, and a number of symbols whose types can be built from the type variables. Some of the state variables of a PSA can be arrays, which are functions from one type to another. We present several new decidability and undecidability results for parameterised control-state reacha- bility problems on subclasses of PSAs.

Relating multiset rewriting and process algebras for security protocol analysis

When formalizing security protocols, different specification languages support very different reasoning methodologies, whose results are not directly or easily comparable. Therefore, establishing clear mappings among different frameworks is highly de

Finding direct partition bijections by two-directional rewriting techniques

One basic activity in combinatorics is to establish combinatorial identities by so-called ‘bijective proofs,’ which consists in constructing explicit bijections between two types of the combinatorial objects under consideration. We show how such bijective proofs can be established in a systematic way from the ‘lattice properties’ of partition ideals, and how the desired bijections are computed by means of multiset rewriting, for a variety of combinatorial problems involving partitions. In particular, we fully characterizes all equinumerous partition ideals with ‘disjointly supported’ complements. This geometrical characterization is proved to automatically provide the desired bijection between partition ideals but in terms of the minimal elements of the order filters, their complements. As a corollary, a new transparent proof, the ‘bijective’ one, is given for all equinumerous classes of the partition ideals of order 1 from the classical book “The Theory of Partitions” by G.Andrews. Establishing the required bijections involves two-directional reductions technique novel in the sense that forward and backward application of rewrite rules heads, respectively, for two different normal forms (representing the two combinatorial types). It is well-known that non-overlapping multiset rules are confluent. As for termination, it generally fails even for multiset rewriting systems that satisfy certain natural invariant balance conditions. The main technical development of the paper (which is important for establishing that the mapping yielding the combinatorial bijection is functional) is that the restricted two-directional strong normalization holds for the multiset rewriting systems in question.

Multiset rewriting and the complexity of bounded security protocols

We formalize the Dolev–Yao model of security protocols, using a notation based on multiset rewriting with existentials. The goals are to provide a simple formal notation for describing security protocols, to formalize the assumptions of the Dolev–Yao

An Overview of MSR( [formula omitted]): A CLP-based Framework for the Symbolic Verification of Parameterized Concurrent Systems

In recent works we have defined a general framework for the validation of parameterized concurrent systems based on the combination of multiset rewriting and constraints. The class of systems we are interested in consists of concurrent systems parametric in the number of individual components.Our framework provides the following features: 1.a specification language for the class of concurrent systems taken into consideration;2.an assertional language to finitely represent infinite sets of configurations; and3.a sound and fully automatic verification method based on symbolic state exploration.The verification procedure has been implemented in a Constraint Logic Programming systems, namely Sicstus Prolog and the clp(Q,R) library. CLP provides in fact all necessary operations to manipulate multisets and constraints both as uninterpreted and interpreted objects. Operations over constraints are delegated in fact to the clp(Q,R) library, and encapsulated into Sicstus Prolog predicates. The method can be applied to solve validation problems for communication protocols, and (potentially) of security and authentication protocols and abstractions of concurrent programs.In this paper we overview the main features of our framework and comment on some of the more interesting applications.

On the expressiveness of coordination via shared dataspaces

A number of different coordination models for specifying inter-process communication and synchronisation rely on a notion of shared dataspace. Many of these models are extensions of the Linda coordination model, which includes operations for adding, deleting and testing the presence/absence of data in a shared dataspace. We compare the expressive power of three classes of coordination models based on shared dataspaces. The first class relies on Linda's communication primitives, while a second class relies on the more general notion of multi-set rewriting (e.g., like Bauhaus Linda or Gamma). Finally, we consider a third class of models featuring communication transactions that consist of sequences of Linda-like operations to be executed atomically (e.g., like in Shared Prolog or PoliS).

Typed Multiset Rewriting Specifications of Security Protocols

The language MSR has successfully been used in the past to prove undecidability results about security protocols modeled according to the Dolev-Yao abstraction. In this paper, we revise this formalism into a flexible specification framework for complex crypto-protocols. More specifically, we equip it with an extensible typing-infrastructure based on dependent types with subsorting, which elegantly captures and enforces basic relations among objects, such as between a public key and its inverse. We also introduce the notion of memory predicate, where principals can store information that survives role termination. These predicates allow specifying complex protocols structured into a coordinated collection of subprotocols. Moreover, they permit describing different attacker models using the same syntax as any other role. We demonstrate this possibility and the precision of our type system by presenting two formalizations of the Dolev-Yao intruder. We discuss two execution models for this revised version of MSR, one sequential and one parallel, and prove that the latter can be simulated by the former.