Complexity, parallel computation and statistical physics

Complexity, parallel computation and statistical physics

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history applicable to systems of the kind studied in statistical physics. It is argued that phys...

Parallel Computational Complexity in Statistical Physics

We suggest the parallel computational complexity of simulating a system as a measure of its physical complexity. As an example, we present a parallel algorithm for simulating diiusion-limited aggregation (DLA) and calculate the algorithm's dynamic exponent z, which gives the scaling of the average running time with cluster radius. It is plausible that the algorithm attains the minimum possible ...

Parallel Computational Complexity and Logical Depth in Statistical Physics

Models of Parallel Computation and Parallel Complexity

This thesis reviews selected topics from the theory of parallel computation. The research begins with a survey of the proposed models of parallel computation. It examines the characteristics of each model and it discusses its use either for theoretical studies, or for practical applications. Subsequently, it employs common simulation techniques to evaluate the computational power of these model...

Statistical Physics into Computational Complexity

NP-complete” problems are at the core of many computational tasks of practical interest, which means that the cost of solution will grow exponentially with problem size in the worst case (provided P NP). Although heuristics can be quite effective on such problems in most cases, there is a growing appreciation that these problems contain phase transitions, and at the phase boundaries exponential...