Seminars

Title: The planar geometry of first-order string transductions (joint work with Pierre Pradic)


Abstract:
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We propose a new machine model recognizing star-free languages, with a geometric flavor. Our starting point is the characterization of regular languages using two-way automata (2DFA). The idea is to take seriously the visual representations found throughout the literature of the behavior of a 2DFA on a word ; by putting a total order on the set of states, one can formally define what it means for such a behavior to be planar, in a sense analogous to the planarity of combinatorial maps. Star-free languages are then exactly the languages recognized by "planar 2DFA". We also show that the corresponding planar transducer model characterizes the class of first-order transductions (a.k.a. aperiodic regular functions). If time allows, the talk will briefly discuss the connections of this work with the non-commutative lambda-calculus (cf. our recent paper Aperiodicity in a non-commutative logic, ICALP'20).