Reduction of Nondeterministic Tree Automata

Abstract

Abstract. We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tree-language inclusion is EXPTIME-complete, we describe methods to compute good approximations in polynomial time. We implemented our algorithm as a module of the well-known libvata tree automata library, and tested its performance on a given collection of tree automata from various applications of libvata in regular model checking and shape analysis, as well as on various classes of randomly generated tree automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances.

Reducing Nondeterministic Tree Automata by Adding Transitions

“…Heavy behaves well in practice, significantly reducing both automata of program verification provenience and randomly generated automata [6].…”

“…Efficient reduction algorithms have been presented both for word automata [8] and for tree automata [2,6], where language inclusion is witnessed by the membership of a pair of states in a simulation preorder. In our paper, we focus on Heavy(x,y) [6], a polynomial-time algorithm for reducing tree automata, in the sense of obtaining a smaller automaton with the same language, though not necessarily with the absolute minimal number of states possible (in general, as with word automata, there is no unique nondeterministic automaton with the minimal possible number of states for a given language). Heavy(x,y) is based on an intricate combination of transition pruning and state quotienting techniques for tree automata, extending previous work on the words case [8].…”

A Congruence-Based Perspective on Finite Tree Automata

“…Like word automata, tree automata (both BTAs and TTAs) can be deterministic (DBTAs and DT-TAs) or non-deterministic, offering the classical trade-off, where deterministic automata are easier to reason about while non-deterministic ones are more concise. This situation has motivated the study of techniques to reduce the number of states of deterministic automata [8,9,10] as well as methods for building deterministic automata that are minimal in the number of states [11,12,13]. For both word and tree automata the minimal deterministic automaton is unique (up to isomorphisms).…”

Minimization of Visibly Pushdown Automata Using Partial Max-SAT

“…Size reduction of automata is an active research topic [15,34,9,16,10,2,4] that is theoretically appealing and has practical relevance: smaller automata require less memory and speed up automata-based tools [28,30,22,24]. In this This paper is an extended version of the paper with the same title presented at TACAS 2017 [27].…”

“…Vpa do not have a canonical minimum [6]. For other automaton classes that lack this property, the usual approach is to find equivalence relations that are sufficient for quotienting [19,1,4]. The main difficulty of a quotienting approach for Vpa is that two states may behave similarly given one stack but differently given another stack, and as the number of stacks is usually infinite, one cannot simply compare the behaviors for each of them.…”