## On a family of L languages resulting from systolic tree automata.(English)Zbl 0549.68081

The class of BT-VLSI languages accepted by binary systolic tree automata contains all rational languages, is closed under Boolean operations, and the equivalence problem is decidable. This paper shows that every BT-VLSI language is an EOL language. In order to describe the relationship between these two classes the notion of a semibinary EOL language is introduced. Every EOL language is the coding of a semibinary EOL language, and an EOL language belongs to BT-VLSI if it is a coding of a semibinary suffix EOL language. On the other hand, the emptiness problem for the class of T-VLSI languages, i.e. the languages accepted by general systolic tree automata, can be reduced to two well-known open problems about $${\mathbb{Z}}$$-rational formal power series. In particular it remains open whether an arbitrary T-VLSI language is an EOL language.
Reviewer: M.Kunze

### MSC:

 68Q45 Formal languages and automata
Full Text:

### References:

 [1] Culik, K., On some families of languages related to developmental systems, Internat. J. comput. math., 4, 31-42, (1974) · Zbl 0294.68025 [2] Culik, K.; Salomaa, A.; Wood, D., VLSI systolic trees as acceptors, () [3] Culik, K.; Gruska, J.; Salomaa, A., Systolic Trellis automata (for VLSI), () · Zbl 0571.68042 [4] Culik, K.; Gruska, J.; Salomaa, A., Systolic automata for VLSI on balanced trees, () · Zbl 0493.68054 [5] Culik, K.; Opatrny, J., Macro OL systems, Internat. J. comput. math., 4, 327-342, (1975) · Zbl 0309.68064 [6] Rozenberg, G.; Salomaa, A., The mathematical theory of L systems, (1980), Academic Press New York · Zbl 0365.68072 [7] Salomaa, A.; Soittola, M., Automata-theoretic aspects of formal power series, (1978), Springer Berlin · Zbl 0377.68039
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