Extended Abstract: Decision Problems on Iterated Length-Preserving Transducers

Finite-state transducers are simple theoretical machines that are useful in expressing easilycomputable functions and relations. This investigation considers the relations formed when transducers are iterated arbitrarily many times, a construction which is useful in model checking. In particular, we consider a number of decision problems over various classes of transducers, and attempt to determine whether each decision problem is decidable. For example, a Turing machine construction can show that the string reachability problem on arbitrary iterated transducers reduces from the halting problem, and is thus undecidable. This setup is useful for investigating how restricted a transducer must be before its iteration is no longer able to simulate a Turing machine (for different notions of simulation). The main result of the paper is that both reset transducers—which have a highly restricted concept of memory—and binary toggle transducers—which must express all letter transformations as permutations—are capable of simulating a Turing machine computation.