Real-time Language Recognition Research Articles

Languages not recognizable in real time by one-dimensional cellular automata

This paper discusses real-time language recognition by one-dimensional cellular automata (CA), focusing on limitations of the parallel recognition power. We investigate language recognition of strings containing binary representations B ( | w | ) of their own lengths. It is shown that: (1) The language L X = { w ∈ { 0 , 1 } + : w contains the binary number(s) B ( | w | ) } is recognizable by CA in linear time, but is not recognizable in real time; and (2) The class of languages that are recognizable by CA in real time is not closed under concatenation and not closed under reversal. These results are solutions to the problems posed by Smith III in [A.R. Smith III, Real-time language recognition by one-dimensional cellular automata, J. Comput. System Sci. 6 (1972) 233–253].

Real-Time Recognition of Cyclic Strings by One-Way and Two-Way Cellular Automata

This paper discusses real-time language recognition by 1dimensional one-way cellular automata (OCAs) and two-way cellular automata (CAs), focusing on limitations of the parallel computation power. To clarify the limitations, we investigate real-time recognition of cyclic strings of the form uk with u ∈ {0, 1}+ and k ≥ 2. We show a version of pumping lemma for recognizing cyclic strings by OCAs, which can be used for proving that several languages are not recognizable by OCAs in real time. The paper also discusses the real-time language recognition of CAs by prefix and postfix computation, in which every prefix or postfix of an input string is also accepted, if the prefix or postfix is in the language. It is shown that there are languages L ⊆ Σ such that L is not recognizable by OCA in real-time and the reversal of L and the concatenation LΣ∗ are recognizable by CA in real-time. key words: cellular automata, OCA, parallel language recognition, pumping lemma, prefix recognition

Dynamical recognizers: real-time language recognition by analog computers

We consider a model of analog computation which can recognize various languages in real time. We encode an input word as a point in R d by composing iterated maps, and then apply inequalities to the resulting point to test for membership in the language. Each class of maps and inequalities, such as quadratic functions with rational coefficients, is capable of recognizing a particular class of languages. For instance, linear and quadratic maps can have both stack-like and queue-like memories. We use methods equivalent to the Vapnik-Chervonenkis dimension to separate some of our classes from each other: linear maps are less powerful than quadratic or piecewise-linear ones, polynomials are less powerful than elementary (trigonometric and exponential) maps, and deterministic polynomials of each degree are less powerful than their non-deterministic counterparts. Comparing these dynamical classes with various discrete language classes helps illuminate how iterated maps can store and retrieve information in the continuum, the extent to which computation can be hidden in the encoding from symbol sequences into continuous spaces, and the relationship between analog and digital computation in general. We relate this model to other models of analog computation; in particular, it can be seen as a real-time, constant-space, off-line version of Blum, Shub and Smale's real-valued machines.

Real-time language recognition by one-dimensional cellular automata

Pattern recognition by parallel devices is investigated by studying the formal language recognition capabilities of one-dimensional cellular automata. The precise relationships of cellular automata to iterative automata and to Turing machines are established: In both cases, cellular automata are inherently faster. The relationship of context-free languages to the languages recognized in real time by bounded cellular automata is detailed. In particular, nondeterministic bounded cellular automata can recognize the context-free languages in real time. The deterministic case remains open, but many partial results are derived. Finally, closure properties and cellular automata transformation lemmas are presented.