Two-Way Sequential Transductions and Stack Automata

A 2-way sequential transducer is a 2-way finite acceptor to which an output structure has been added. Such a device is considerably more complex than the usual 1-way sequential transducer, and it is shown that these transducers map both regular sets and context free languages into the context sensitive languages. Such a transducer is the simplest known which can map a list into its reversal or make duplicate copies of a list. In this paper unsolvability of equivalence is shown for a special class of nondeterministic 2-way sequential transducers, and it is shown that deterministic transducers are not so powerful as nondeterministic transducers. The properties of two-way transductions of regular-sets and context free languages are derived in detail and are shown to be similar to the corresponding properties of context free languages. Also, in this paper the intimate relationship between 2-way sequential transducers and 1-way stack automata is shown by presenting a new grammar which generates exactly the 1-way stack automata languages, and many of the properties of these grammars are derived.

[1]  John C. Shepherdson,et al.  The Reduction of Two-Way Automata to One-Way Automata , 1959, IBM J. Res. Dev..

[2]  Peter S. Landweber,et al.  Decision Problems of Phrase-Structure Grammars , 1964, IEEE Trans. Electron. Comput..

[3]  Jeffrey D. Ullman,et al.  Two Results on One-Way Stack Automata , 1967, SWAT.

[4]  Seymour Ginsburg,et al.  One-way stack automata , 1967, JACM.

[5]  Noam Chomsky,et al.  On Certain Formal Properties of Grammars , 1959, Inf. Control..

[6]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[7]  Alfred V. Aho.  Indexed Grammars-An Extension of Context Free Grammars , 1967, SWAT.

[8]  Mario Schkolnick,et al.  Two-Type Bracketed Grammars , 1968, SWAT.

[9]  Seymour Ginsburg,et al.  The mathematical theory of context free languages , 1966 .

[10]  Jeffrey D. Ullman,et al.  Formal languages and their relation to automata , 1969, Addison-Wesley series in computer science and information processing.

[11]  Timothy V. Griffiths.  The unsolvability of the Equivalence Problem for Λ-Free nondeterministic generalized machines , 1968, JACM.

[12]  Sik-Sang Yau.  TWO-WAY SEQUENTIAL TRANSDUCERS AND STACK AUTOMATA , 1969 .

[13]  Seymour Ginsburg,et al.  Stack automata and compiling , 1967, JACM.

[14]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[15]  S.-Y. Kuroda,et al.  Classes of Languages and Linear-Bounded Automata , 1964, Inf. Control..