P. Orponen, Computational complexity of neural networks: A survey, Nordic Journal of Computing 1 (1) (1994) 94--110.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and continuous time to point out alternative sources of efficient computation. 1 Introduction The computational potential and limits of neural networks have been studied for more than a decade in order to understand what is, either ultimately or efficiently, computable by particular models [15, 28, 48, 50, 53, 54, 55, 56, 58, 61, 67, 72]. This interest is motivated partly by the quest to formally justify heuristics used in practical neurocomputing, and partly by the realization that despite their formal simplicity, neural networks are computationally quite powerful, and thus may serve as a useful reference model for investigating ....

P. Orponen, Computational complexity of neural networks: A survey, Nordic Journal of Computing 1 (1) (1994) 94--110.

.... models of computation such as Turing machines which are useful for understanding the computational potential and limits of conventional computers, the capability of neural networks to realize general computations have been studied for more than decade and many relevant results have been achieved [25, 44, 84, 88, 92, 93, 94, 103, 108, 123, 131]. In particular, the computational and descriptive power of neural nets have been investigated by comparing their various architectures with each other and with more traditional computational models and descriptive tools including nite automata, regular expressions, grammars, Turing machines, ....

P. Orponen, Computational complexity of neural networks: A survey, Nordic Journal of Computing 1 (1) (1994) 94-110.

.... (nonlinear control) Blondel and Tsitsiklis, 1998] elementary nonlinear systems) Littman et al. 1995] Rust, 1996] Mundhenk et al. 1997] Markov decision theory) Alur et al. 1995] hybrid systems) Bournez and Cosnard, 1996] Moore, 1998] Turing machine as dynamical systems) and [Orponen, 1994] (recurrent neural networks) Some open problems related to the computational complexity of control questions are proposed in [Blondel et al. 1999c, Problems 11, 14, 22, and 43] 2 Complexity theory In this section, we introduce the main concepts from the theory of computability and complexity, ....

Orponen, P. (1994). Computational complexity of neural networks: a survey, Nordic Journal of Computing, 1, 94-100.

....As a consequence, the same result for a neuromaton equivalence problem is achieved. 1 Introduction Neural networks [7] are models of computation motivated by our ideas about brain functioning. Both their computational power and their efficiency have been traditionally investigated [4, 14, 15, 19, 21] within the framework of computer science. One less commonly studied task which we will be addressing is the comparison of the computational power of neural networks with the traditional finite models of computation, such as recognizers of regular languages. It appears that a finite This ....

Orponen, P. 1994. Computational Complexity of Neural Networks: A Survey. Nordic Journal of Computing, 1, 94--110.

....and limits of conventional computers are by now well understood in terms of classical models of computation such as Turing machines. Analogously, many fundamental results have been achieved in the past decade concerning the capabilities of neural networks for general computation [26] 45] 86] [90], 94] 95] 96] 105] 110] 128] 136] In particular, the computational and descriptive powers of neural nets have been investigated by comparing their various architectures with each other and with more traditional computational models and descriptive tools such as nite automata, ....

P. Orponen, Computational complexity of neural networks: A survey, Nordic Journal of Computing 1 (1) (1994) 94-110.

....networks [29, 30] In this overview, we focus on the computational power of recurrent (cyclic) neural networks. The computational study of feedforward (acyclic) networks has intimate connections to the classical theory of Boolean circuit complexity [53] and is surveyed brie y in the articles [36, 40], and at greater depth in the books [41, 43, 52] 2. BASIC NOTIONS AND RESULTS With the brief exception of Section 6 on continuous time models, we shall be concerned with nite discrete time recurrent networks. Such a network consists of n computational units or neurons, indexed as 1; n, ....

Orponen, P. Computational complexity of neural networks: A survey. Nordic Journal of Computing 1 (1994), 94-110.

....[12] exponential transient network as a clock . For general surveys of automata networks, see the books [5, 9] Threshold logic networks have recently become (again) popular as discrete models of neural networks. Computational aspects of these models are discussed in, e.g. the survey papers [17, 18, 26], and in the books [14, 19, 20, 22] 2 Preliminaries A threshold logic network (or a binary recurrent neural network ) consists of n threshold logic units (or binary neurons ) each of which is at a given moment in either one of two states x i = 1 or x i = 0, also called the on and off states. ....

Orponen, P. Computational complexity of neural networks: A survey. Nordic Journal of Computing 1 (1994), 94--110.

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