We extend a classic result of Buchi, Elgot, and Trakhtenbrot: MSO definable string transductions i.e., string-to-string functions that are definable by an interpretation using monadic second-order (MSO) logic, are exactly those realized by deterministic two-way finite-state transducers, i.e., finite-state automata with a two-way input tape and a one-way output tape. Consequently, the equivalence of two mso definable string transductions is decidable. In the nondeterministic case however, MSO definable string tranductions, i.e., binary relations on strings that are mso definable by an interpretation with parameters, are incomparable to those realized by nondeterministic two-way finite-state transducers. This is a motivation to look for another machine model, and we show that both classes of MSO definable string transductions are characterized in terms of Hennie machines, i.e., two-way finite-state transducers that are allowed to rewrite their input tape, but may visit each position of their input only a bounded number of times.

MSO definable string transductions and two-way finite-state transducers

https://ris.utwente.nl/ws/files/6563661/Engelfriet80tree.pdf

Tree Transducers, L Systems, and Two-Way Machines

Composition of top-down tree transducers yields a proper hierarchy of transductions and of output languages. The same is true for ETOL systems (viewed as transducers) and for two-way generalized sequential machines.

/pdf/three-hierarchies-of-transducers-inae7b1mlq.pdf

Three hierarchies of transducers

An iterated pushdown is a pushdown of pushdowns of … of pushdowns. An iterated exponential function is 2 to the 2 to the … to the 2 to some polynomial. The main result presented here is that the nondeterministic 2-way and multi-head iterated pushdown automata characterize the deterministic iterated exponential time complexity classes. This is proved by investigating both nondeterministic and alternating auxiliary iterated pushdown automata, for which similar characterization results are given. In particular it is shown that alternation corresponds to one more iteration of pushdowns. These results are applied to the 1-way iterated pushdown automata: (1) they form a proper hierarchy with respect to the number of iterations, and (2) their emptiness problem is complete in deterministic iterated exponential time. Similar results are given for iterated stack (checking stack, nonerasing stack, nested stack, checking stack-pushdown) automata.

Donald I. Kiel

Papers

Two-way a-transducers and AFL