2020/08/03 by Lê Thành Dũng Nguyễn, Camille Noûs, Nguyên, Lê Thành Dũng +2
Computer Science · #03B40 #03B70 #68Q45 #Computability, Logic, AI Algorithms #F.4.1 #F.4.3 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2008.01050
openalex publication_date 2020/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize regular string transductions as programs in a linear λ-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions, into our λ-calculus. For the converse, we consider a categorical framework for defining automata and transducers over words, which allows us to relate register updates in SSTs to the semantics of the linear λ-calculus in a suitable monoidal closed category. To illustrate the relevance of monoidal closure to automata theory, we also leverage this notion to give abstract generalizations of the arguments showing that copyless SSTs may be determinized and that the composition of two regular functions may be implemented by a copyless SST. Our main result is then generalized from strings to trees using a similar approach. In doing so, we exhibit a connection between a feature of streaming tree transducers and the multiplicative/additive distinction of linear logic. Keywords: MSO transductions, implicit complexity, Dialectica categories, Church encodings