Register automata with linear arithmetic
Yu‐Fang Chen, Ondřej Lengál, Tony Tan, Zhilin Wu · 2017
We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RAℚ). It reads a sequence of rational numbers and outputs another rational number. RAℚis an extension of the well-known register automata (RA) over infinite alphabets, which are finite automata equipped with a finite number of registers/variables for storing values. Like in the standard RA, the RAℚmodel allows both equality and ordering tests between values. It, moreover, allows to perform linear arithmetic between certain variables. The model is quite expressive: in addition to the standard RA, it also generalizes other well-known models such as affine programs and arithmetic circuits. The main feature of RAℚis that despite the use of linear arithmetic, the so-called invariant problem-a generalization of the standard non-emptiness problem-is decidable. We also investigate other natural decision problems, namely, commutativity, equivalence, and reachability. For deterministic RAℚ, commutativity and equivalence are polynomial-time inter-reducible with the invariant problem.