Related papers: Non-Global Parikh Tree Automata
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…
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 study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
Monitored many-body systems can exhibit a phase transition between entangling and disentangling dynamical phases by tuning the strength of measurements made on the system as it evolves. This phenomenon is called the measurement-induced…
Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain…
In many kinds of infinite-state systems, the coverability problem has significantly lower complexity than the reachability problem. In order to delineate the border of computational hardness between coverability and reachability, we propose…
We transfer distances on clusterings to the building process of decision trees, and as a consequence extend the classical ID3 algorithm to perform modifications based on the global distance of the tree to the ground truth--instead of…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such…
This short note aims at proving that the isolation problem is undecidable for probabilistic automata with only one probabilistic transition. This problem is known to be undecidable for general probabilistic automata, without restriction on…
We present a new algorithm, Fractional Decomposition Tree (FDT) for finding a feasible solution for an integer program (IP) where all variables are binary. FDT runs in polynomial time and is guaranteed to find a feasible integer solution…
The P\'olya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial…
We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not…
Randomized fault-tolerant consensus protocols with common coins are widely used in cloud computing and blockchain platforms. Due to their fundamental role, it is vital to guarantee their correctness. Threshold automata is a formal model…
Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes…
This work is a study of the expressive power of unambiguity in the case of automata over infinite trees. An automaton is called unambiguous if it has at most one accepting run on every input, the language of such an automaton is called an…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…