Coherent Parallelization of Universal Classical Computation

Previously, higher-order Hamiltonians (HoH) had been shown to offer an advantage in both metrology and quantum energy storage. Here, we axiomatize a model of computation that allows us to consider such Hamiltonians for the purposes of computation. From this axiomatic model, we formally prove that an HoH-based algorithm can gain up to a quadratic speed-up over classical sequential algorithms—for any possible classical computation. We show how our axiomatic model is grounded in the same physics as that used in HoH-based quantum advantage for metrology and battery charging. Thus we argue that any advance in implementing HoH-based quantum advantage in those scenarios can be co-opted for the purpose of speeding up computation.

Alan Turing and Human-Like Intelligence

Alan Turing’s model of computation (1936) is explicated in terms of the potential operations of a human “computer”, and his famous test for intelligence (1950) is based on indistinguishability from human verbal behaviour. But this chapter challenges the apparent human-centredness of the 1936 model, suggesting a focus instead on mathematical concepts, with human comparisons making an entrance only retrospectively. The 1950 account of intelligence also turns out to be far less human-centred than it initially appears to be, because the universality of computation makes human intelligence just one variety amongst many. It is only when Turing considers consciousness that he treats intelligence in a way that cannot properly be carried over to machines. But here he is mistaken, since his own work gave ample reason to reinterpret intelligence as sophisticated information processing for some purpose, and to divorce this from the subjective consciousness with which it is humanly associated.

Correlations for computation and computation for correlations

Quantum correlations are central to the foundations of quantum physics and form the basis of quantum technologies. Here, our goal is to connect quantum correlations and computation: using quantum correlations as a resource for computation—and vice versa, using computation to test quantum correlations. We derive Bell-type inequalities that test the capacity of quantum states for computing Boolean functions within a specific model of computation and experimentally investigate them using 4-photon Greenberger–Horne–Zeilinger (GHZ) states. Furthermore, we show how the resource states can be used to specifically compute Boolean functions—which can be used to test and verify the non-classicality of the underlying quantum states. The connection between quantum correlation and computability shown here has applications in quantum technologies, and is important for networked computing being performed by measurements on distributed multipartite quantum states.

Watson–Crick Jumping Finite Automata: Combination, Comparison and Closure

A new model of computation called Watson–Crick jumping finite automata was introduced by Mahalingam et al., and the authors study the computing power and closure properties of the variants of the model. There are four variants of the model: no state, 1-limited, all-final and simple Watson–Crick jumping finite automata. In this paper, we introduce a restricted version that is a combination of variants of the existing model. It becomes essential to explore the computing power and closure properties of these combinations. The combination variants are extensively compared with Chomsky hierarchy, general jumping finite automata family and among themselves. We also explore the closure properties of such restricted automata.

What Supercomputing Will Be Like in the Coming Years

This chapter is an abridged sort of “vision statement” on what supercomputing will be in the future. The main thrust of the argument is that most of the problem lies in the trafficking of data, not the computation. There needs to be a worldwide effort to put into place a means to move data efficiently and effectively. Further, there likely needs to be a fundamental shift in our model of computation where the computation is stationary and data moves to movement of computation to the data or even as the data is moving.

Synchronizing Almost-Group Automata

In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing (unless they have one state). In almost-group automata, one of the letters acts as a permutation on [Formula: see text] states, and the others as permutations. We prove that this small change is enough for automata to become synchronizing with high probability. More precisely, we establish that the probability that a strongly-connected almost-group automaton is not synchronizing is [Formula: see text], for a [Formula: see text]-letter alphabet. We also present an efficient algorithm that decides whether a strongly-connected almost-group automaton is synchronizing. For a natural model of computation, we establish a [Formula: see text] worst-case lower bound for this problem ([Formula: see text] for the average case), which is almost matched by our algorithm.

Dendrite P Systems Toolbox: Representation, Algorithms and Simulators

Dendrite P systems (DeP systems) are a recently introduced neural-like model of computation. They provide an alternative to the more classical spiking neural (SN) P systems. In this paper, we present the first software simulator for DeP systems, and we investigate the key features of the representation of the syntax and semantics of such systems. First, the conceptual design of a simulation algorithm is discussed. This is helpful in order to shade a light on the differences with simulators for SN P systems, and also to identify potential parallelizable parts. Second, a novel simulator implemented within the P-Lingua simulation framework is presented. Moreover, MeCoSim, a GUI tool for abstract representation of problems based on P system models has been extended to support this model. An experimental validation of this simulator is also covered.