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Advancing Research in Information and Communication Technology

Part of the book series: IFIP Advances in Information and Communication Technology ((Festschrifts,volume 600))

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Abstract

Descriptional complexity has historically been a multidisciplinary area of study, with contributions from automata theory, computational complexity, cryptography, information theory, probability, statistics, pattern recognition, machine learning, computational learning theory, computer vision, neural networks, formal languages and other fields. Some basic questions are: How succinctly can a descriptional system represent objects (for example, encoded as formal languages) in comparison with other descriptional systems? What is the maximal size trade-off when changing from one system to another, and can it be achieved?

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Notes

  1. 1.

    The 2DFA we described for \(I_n\) makes use of the endmarkers, while the 2DFA for \(L_n\) does not use them. Actually, we could adapt the technique used to recognize \(L_n\) in order to obtain a 2DFA with O(n) states accepting \(I_n\), without using the endmarkers. The main difference is that the 2DFA so obtained may need to reverse the direction of its head many times, while the 2DFA we described for \(I_n\) makes only one reversal. It seems quite natural to have endmarkers in two-way automata. However, in some works they are presented without endmarkers. This does not change the computational power. The example of \(I_n\) shows some differences when we consider size and number of reversals. In general, it has been proved that two-way automata can have different properties with or without endmarkers [90].

  2. 2.

    Concerning the unary case, the state cost of simulation of one-way nondeterministic automata by 2DFAs has been proved to be quadratic [17]. This gives a positive answer to the second question in the unary case.

  3. 3.

    It can be easily seen that each context free-language can be accepted by a pushdown automaton which uses an amount of pushdown store which is linear in the input length.

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  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib

  2. CMUP and DCC, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 4169-007, Porto, Portugal

    Nelma Moreira & Rogério Reis

  3. Dipartimento di Informatica, Università degli Studi di Milano, via Celoria 18, 20133, Milano, Italy

    Giovanni Pighizzini

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Kutrib, M., Moreira, N., Pighizzini, G., Reis, R. (2021). Hot Current Topics of Descriptional Complexity. In: Goedicke, M., Neuhold, E., Rannenberg, K. (eds) Advancing Research in Information and Communication Technology. IFIP Advances in Information and Communication Technology(), vol 600. Springer, Cham. https://doi.org/10.1007/978-3-030-81701-5_1

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