323 research outputs found
Playing with Derivation Modes and Halting Conditions
In the area of P systems, besides the standard maximally parallel derivation
mode, many other derivation modes have been investigated, too. In this paper, many
variants of hierarchical P systems and tissue P systems using different derivation modes
are considered and the effects of using di erent derivation modes, especially the maximally
parallel derivation modes and the maximally parallel set derivation modes, on the
generative and accepting power are illustrated. Moreover, an overview on some control
mechanisms used for (tissue) P systems is given.
Furthermore, besides the standard total halting mode, we also consider different halting
conditions such as unconditional halting and partial halting and explain how the use
of different halting modes may considerably change the computing power of P systems
and tissue P systems
Design and optimisation of scientific programs in a categorical language
This thesis presents an investigation into the use of advanced computer languages for scientific computing, an examination of performance issues that arise from using such languages for such a task, and a step toward achieving portable performance from compilers by attacking these problems in a way that compensates for the complexity of and differences between modern computer architectures. The language employed is Aldor, a functional language from computer algebra, and the scientific computing area is a subset of the family of iterative linear equation solvers applied to sparse systems. The linear equation solvers that are considered have much common structure, and this is factored out and represented explicitly in the lan-guage as a framework, by means of categories and domains. The flexibility introduced by decomposing the algorithms and the objects they act on into separate modules has a strong performance impact due to its negative effect on temporal locality. This necessi-tates breaking the barriers between modules to perform cross-component optimisation. In this instance the task reduces to one of collective loop fusion and array contrac
Physical (A)Causality: Determinism, Randomness and Uncaused Events
Physical indeterminism; Randomness in physics; Physical random number generators; Physical chaos; Self-reflexive knowledge; Acausality in physics; Irreducible randomnes
Formal Verification of P Systems
Membrane systems, also known as P systems, constitute an innovative computational paradigm inspired by the structure and dynamics of the living cell. A P system consists of a hierarchical arrangement of compartments and a finite set of multiset rewriting and communication rules, which operate in a maximally parallel manner. The organic vision of concurrent dynamics captured by membrane systems stands in antithesis with conventional formal modelling methods which focus on algebraic descriptions of distributed systems. As a consequence, verifying such models in a mathematically rigorous way is often elusive and indeed counter-intuitive when considering established approaches, which generally require sequential process representations or highly abstract theoretical frameworks. The prevalent investigations with this objective in the field of membrane computing are ambivalent and inconclusive in the wider application scope of P systems.
In this thesis we directly address the formal verification of membrane systems by means of model checking. A fundamental distinction between the agnostic perspective on parallelism, advocated by process calculi, and P systems' emblematic maximally parallel execution strategy is identified. On this basis, we establish that an intuitional translation to traditional process models is inadequate for the purpose of formal verification, due to a state space growth disparity. The observation is essential for this research project: on one hand it implies the feasibility of model checking P systems, and on the other hand it underlines the suitability of this formal verification technique in the context of membrane computing. Model checking entails an exhaustive state space exploration and does not derive inferences based on the independent instructions comprising a state transition. In this respect, we define a new sequential modelling strategy which is optimal for membrane systems and targets the SPIN formal verification tool.
We introduce elementary P systems, a distributed computational model which subsumes the feature diversity of the membrane computing paradigm and distils its functional vocabulary. A suite of supporting software tools which gravitate around this formalism has also been developed, comprising of 1. the eps modelling language for elementary P systems; 2. a parser for the eps specification; 3. a model simulator and 4. a translation tool which targets the Promela specification of the SPIN model checker.
The formal verification approach proposed in this thesis is progressively demonstrated in four heterogeneous case studies, featuring 1. a parallel algorithm applicable to a structured model; 2. a linear time solution to an NP-complete problem; 3. an innovative implementation of the Dining Philosophers scenario (a synchronisation problem) using an elementary P system and 4. a quantitative analysis of a simple random process implemented without the support of a probabilistic model
Connectivity preserving network transformers
The Population Protocol model is a distributed model that concerns systems of
very weak computational entities that cannot control the way they interact. The
model of Network Constructors is a variant of Population Protocols capable of
(algorithmically) constructing abstract networks. Both models are characterized
by a fundamental inability to terminate. In this work, we investigate the
minimal strengthenings of the latter that could overcome this inability. Our
main conclusion is that initial connectivity of the communication topology
combined with the ability of the protocol to transform the communication
topology plus a few other local and realistic assumptions are sufficient to
guarantee not only termination but also the maximum computational power that
one can hope for in this family of models. The technique is to transform any
initial connected topology to a less symmetric and detectable topology without
ever breaking its connectivity during the transformation. The target topology
of all of our transformers is the spanning line and we call Terminating Line
Transformation the corresponding problem. We first study the case in which
there is a pre-elected unique leader and give a time-optimal protocol for
Terminating Line Transformation. We then prove that dropping the leader without
additional assumptions leads to a strong impossibility result. In an attempt to
overcome this, we equip the nodes with the ability to tell, during their
pairwise interactions, whether they have at least one neighbor in common.
Interestingly, it turns out that this local and realistic mechanism is
sufficient to make the problem solvable. In particular, we give a very
efficient protocol that solves Terminating Line Transformation when all nodes
are initially identical. The latter implies that the model computes with
termination any symmetric predicate computable by a Turing Machine of space
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