Related papers: Optimised determinisation and completion of finite…
This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…
Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…
Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable.…
We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski's style minimization algorithm for tree automata. First, we prove correct this method…
We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm…
We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…
We introduce saturation of nondeterministic tree automata, a technique that consists of adding new transitions to an automaton while preserving its language. We implemented our algorithm on minotaut - a module of the tree automata library…
Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we…
Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the…
In this work, we present multiple new optimizations and heuristics for the determinization of B\"uchi automata that exploit a number of semantic and structural properties, most of which may be applied together with any determinization…
The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique…
Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of…
We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…
We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key…
A register automaton is a finite automaton with finitely many registers ranging from an infinite alphabet. Since the valuations of registers are infinite, there are infinitely many configurations. We describe a technique to classify…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
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…
Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run…