Automata theory in nominal sets

Abstract

Abstract. We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize nominal sets due to Gabbay and Pitts.

WQO Dichotomy for 3-Graphs

“…Net models similar to Petri nets with data have been continuously proposed since the 80s, including, among the others, high-level Petri nets [13], colored Petri nets [17], unordered and ordered data nets [21], ν-Petri nets [25], and constraint multiset rewriting [5,8,9]. Petri nets with data can be also considered as a reinterpretation of the classical definition of Petri nets in sets with atoms [3,4], where one allows for orbit-finite sets of places and transitions instead of just finite ones. The decidability and complexity of standard problems for Petri nets over various data domains has attracted a lot of attention recently, see for instance [14,21,22,24,25].…”

Bisimilarity in Fresh-Register Automata

“…We let 0 ∼ be the whole of U. Then, for all i ∈ ω and h ∈ [0, 2r] ∪ {∞}, 6 We say that (q 1 , S 1 , σ, q 2 , S 2 , h) satisfies the (FSYS) conditions in R.…”

Locally Finite Constraint Satisfaction Problems

“…We choose to define our sets by first order formulas, but all results we show here could be reformulated in terms of group actions, orbit-finite sets and finite supports, studied in [21]. In fact, we used that terminology in most previous work on computation theory over sets with atoms [10], [23], [24], of which the present paper is a natural continuation.…”

“…The notions of action, equivariance and orbits, can be developed as previously, with Aut(A) replaced by Aut(A, <) throughout, and definable sets replaced by order definable sets. (This is a special case of a construction from [23], where various "atom symmetries" are considered, which is itself a special case of permutation models studied in set theory.) To distinguish from previous notions, we shall speak of monotone-equivariant sets and functions.…”