相关论文: Physical Complexity of Symbolic Sequences

This paper examines several measures of space complexity of variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept every word in the language of…

Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…

We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their…

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…

In this paper we analyze the notion of "stopping time complexity", informally defined as the amount of information needed to specify when to stop while reading an infinite sequence. This notion was introduced by Vovk and Pavlovic (2016). It…

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…

We consider a simplified version of a solvable model by Mandal and Jarzynski, which constructively demonstrates the interplay between work extraction and the increase of the Shannon entropy of an information reservoir which is in contact…

We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an…

We provide tight upper and lower bounds on the expected minimum Kolmogorov complexity of binary classifiers that are consistent with labeled samples. The expected size is not more than complexity of the target concept plus the conditional…

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…

Complexity in engineered systems presents one of the most persistent challenges in modern development since it is driving cost overruns, schedule delays, and outright project failures. Yet while architectural complexity has been studied,…

We study the asymptotic behaviour of symbolic computing systems, notably one-dimensional cellular automata (CA), in order to ascertain whether and at what rate the number of complex versus simple rules dominate the rule space for increasing…

The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…

The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual…

This paper considers a finite sample perspective on the problem of identifying an LTI system from a finite set of possible systems using trajectory data. To this end, we use the maximum likelihood estimator to identify the true system and…

We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…

We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…