Related papers: Fixpoint Node Selection Query Languages for Trees
In this paper we describe an approach to constraint-based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
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…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
Monadic Second-Order Logic (MSO) extends First-Order Logic (FO) with variables ranging over sets and quantifications over those variables. We introduce and study Monadic Tree Logic (MTL), a fragment of MSO interpreted on infinite-tree…
We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and first-order logic over…
In this paper, we study First Order Logic (FO) over (unordered) infinite trees and its connection with branching-time temporal logics. More specifically, we provide an automata-theoretic characterisation of FO interpreted over infinite…
We study the problem of enumerating the answers to a query formulated in monadic second order logic (MSO) over an unranked forest F that is compressed by a straight-line program (SLP) D. Our main result states that this can be done after…
We study the expressive power and succinctness of order-invariant sentences of first-order (FO) and monadic second-order (MSO) logic on structures of bounded tree-depth. Order- invariance is undecidable in general and, thus, one strives for…
In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query…
Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary…
Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for…
In response to the lack of trust in Artificial Intelligence (AI) for sequential planning, we design a Computational Tree Logic-guided large language model (LLM)-based natural language explanation framework designed for the Monte Carlo Tree…
We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte…
A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…
Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a…