Related papers: On Reversible Transducers
Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on…
Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities,…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
The theory of regular and aperiodic transformations of finite strings has recently received a lot of interest. These classes can be equivalently defined using logic (Monadic second-order logic and first-order logic), two-way machines…
We introduce a flow condition on open graph states (graph states with inputs and outputs) which guarantees globally deterministic behavior of a class of measurement patterns defined over them. Dependent Pauli corrections are derived for all…
A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…
We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing a new result even in the unweighted setting…
Call a string-to-string transducer regular if it can be realised by one of the following equivalent models: mso transductions, two-way deterministic automata with output, and streaming transducers with registers. This paper proposes to…
Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…
We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation is definable (1)~by a linear top-down tree transducer or (2)~by a tree homomorphism. We present algorithms that…
We prove that functionality of compositions of top-down tree transducers is decidable by reducing the problem to the functionality of one top-down tree transducer with look-ahead.
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
Deterministic 2-head finite automata which are machines that process an input word from both ends are analyzed for their ability to perform reversible computations. This implies that the automata are backward deterministic, enabling unique…
This paper introduces a robust class of functions from finite words to integers that we call Z-polyregular functions. We show that it admits natural characterizations in terms of logics, Z-rational expressions, Z-rational series and…
Deterministic two-way transducers define the class of regular functions from words to words. Alur and Cern\'y introduced an equivalent model of transducers with registers called copyless streaming string transducers. In this paper, we drop…
We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it…
We present a construction for the composition of subsequential transducers (representing conditional probabilistic models) with subsequential failure transducers (representing probabilistic models). Under certain conditions, satisfied by…