相关论文: Constraint Automata on Infinite Data Trees: From C…

We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…

It is well known that (timed) $\omega$-regular properties such as `p holds at every even position' and `p occurs at least three times within the next 10 time units' cannot be expressed in Metric Interval Temporal Logic ($\mathsf{MITL}$) and…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

LTL synthesis -- the construction of a function to satisfy a logical specification formulated in Linear Temporal Logic -- is a 2EXPTIME-complete problem with relevant applications in controller synthesis and a myriad of artificial…

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e.,…

Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes coincides with an important dichotomy in universal algebra; in…

We study the expressive power of First-Order Logic (\FO) over (unordered) infinite trees, with the aim of identifying robust characterisations in terms of branching-time specification formalisms. While such correspondences are well…

Parikh (tree) automata are an expressive and yet computationally well-behaved extension of finite automata -- they allow to increment a number of counters during their computations, which are finally tested by a semilinear constraint. In…

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…

We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property…

This paper examines the complexity of hybrid logics over transitive frames, transitive trees, and linear frames. We show that satisfiability over transitive frames for the hybrid language extended with the downarrow operator is…

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…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

The aim of this work is to thoroughly investigate Buchi automata augmented with spatial constraints. The input trees of such an automaton are infinite k-ary Sigma-trees, with the nodes standing for time points, and Sigma including,…

Formal XAI (explainable AI) is a growing area that focuses on computing explanations with mathematical guarantees for the decisions made by ML models. Inside formal XAI, one of the most studied cases is that of explaining the choices taken…

This paper shows that the satisfiability problem for probabilistic CTL (PCTL, for short) is undecidable. By a reduction from $1\frac{1}{2}$-player games with PCTL winning objectives, we establish that the PCTL satisfiability problem is…

Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…

We introduce a new class of automata (which we coin EU-automata) running on infininte trees of arbitrary (finite) arity. We develop and study several algorithms to perform classical operations (union, intersection, complement, projection,…

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…

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent real-time extensions of Linear Temporal Logic (LTL). In general, the satisfiability checking problem for these extensions is undecidable when both the…