Non-recursive trade-offs between two-dimensional automata and grammars

作者：Prusa Daniel^*

来源：Theoretical Computer Science, 2016, 610: 121-132.

DOI：10.1016/j.tcs.2015.05.033

• Picture languages
• Four-way automata
• Two-dimensional context-free grammars
• Descriptional complexity
• Non-recursive trade-offs

We study succinctness of descriptional systems for picture languages. Basic models of two-dimensional finite automata and generalizations of context-free grammars are considered. They include the four-way automaton of Blum and Hewitt, the two-dimensional online tessellation automaton of Inoue and Nakamura and the context-free Kolam grammar of Siromoney et al. We show that non-recursive trade-offs between the systems are very common. Basically, each separation result proving that one system describes a picture language which cannot be described by another system can usually be turned into a non-recursive trade-off result between the systems. These findings are strongly based on the ability of the systems to simulate Turing machines.

• 出版日期2016-1-11