SIAM Journal on Computing
Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Introduction to Formal Language Theory
Introduction to Formal Language Theory
The Mathematical Theory of Context-Free Languages
The Mathematical Theory of Context-Free Languages
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
On recursive and non-recursive trade-offs between finite-turn pushdown automata
Journal of Automata, Languages and Combinatorics
| Hi-index | 0.00 |
We investigate finite-turn pushdown automata (PDAs) from the point of view of descriptional complexity. It is known that such automata accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-off. In this paper, we consider finite-turn PDAs that can accept bounded languages. First, we study letter-bounded languages and prove that, in this case, the non-recursive trade-off is reduced to a recursive trade-off, more precisely, to an exponential trade-off. We present a conversion algorithm and show the optimality of the construction by proving tight lower bounds. Furthermore, we study the question of reducing the number of turns of a given finite-turn PDA. Again, we provide a conversion algorithm which shows that, in this case, the trade-off is at most polynomial. Finally, we investigate the more general case of word-bounded languages and show how the results obtained for letter-bounded languages can be extended to word-bounded languages.