2015/04/15 by Ismaël Jecker, Jecker, Ismaël, Emmanuel Filiot +1
Computer Science · #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.FL
paper · pdf · doi:10.48550/arxiv.1504.03864
23 pages
arxiv created 2015/04/15 · arxiv updated 2015/04/16
Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A particular kind of rational relations is the sequential functions. Sequential functions are the functions that can be realised by input-deterministic transducers. Some rational functions are not sequential. However, based on a property on transducers called the twinning property, it is decidable in PTime whether a rational function given by an NFT is sequential. In this paper, we investigate the generalisation of this result to multi-sequential relations, i.e. relations that are equal to a finite union of sequential functions. We show that given an NFT, it is decidable in PTime whether the relation it defines is multi-sequential, based on a property called the weak twinning property. If the weak twinning property is satisfied, we give a procedure that effectively constructs a finite set of input-deterministic transducers whose union defines the relation. This procedure generalises to arbitrary NFT the determinisation procedure of functional NFT.