String-to-String Interpretations With Polynomial-Size Output

Pebble Minimization of Polyregular Functions

“…The two results put together entail that we can decide if a polyregular function is regular. Overall we have obtained a quite satisfying understanding of the growth of polyregular functions, at least in two of the five different models presented in [Bojańczyk 2018;Bojańczyk et al 2019].…”

“…We have shown that the number of pebbles of pebble transducers exactly coincides with the growth degree of polyregular functions. As a corollary, using [Bojańczyk et al 2019], we obtain that interpretations of dimension k compute the same functions as k-pebble transducers. Moreover, we have shown how to minimize the number of pebbles of pebble transducers.…”

“…1 The definition of interpretation used in [Bojańczyk et al 2019] is slightly different: they do not make use of copying. This difference does not change expressiveness, up to increasing the dimension by 1.…”

“…Polyregular functions have been shown to be characterized by many different computational models [Bojańczyk 2018;Bojańczyk et al 2019]. The model we are interested in is that of pebble transducers which are automata that can place pebbles on a bounded number of positions following a stack discipline, meaning that only the most recently placed pebble can be moved.…”

Pebble-Depth

“…Specifically we examine the class of functions known as polyregular functions. While there are several equivalent characterisations of polyregular functions [4,5], we examine the characterisation given by a restricted class of pebble transducers. For k ∈ N, a k-pebble transducer is a two-way finite-state transducer with the additional capacity to mark k squares of its tape with its pebbles.…”