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There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…
The tree automaton completion is an algorithm used for proving safety properties of systems that can be modeled by a term rewriting system. This representation and verification technique works well for proving properties of infinite systems…
We study preprocessing techniques for clause normal forms of LTL formulas. Applying the mechanism of labelled clauses enables us to reinterpret LTL satisfiability as a set of purely propositional problems and thus to transfer simplification…
This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the field Q of rational numbers. We use polynomial identity testing and the Isolation Lemma to obtain…
Synthesis techniques take realizable Linear Temporal Logic specifications and produce correct cir- cuits that implement the specifications. The generated circuits can be used directly, or as miters that check the correctness of a logic…
Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
Virtually all verification and synthesis techniques assume that the formal specifications are readily available, functionally correct, and fully match the engineer's understanding of the given system. However, this assumption is often…
Research in robotic planning with temporal logic specifications, such as Linear Temporal Logic (LTL), has relied on single formulas. However, as task complexity increases, LTL formulas become lengthy, making them difficult to interpret and…
In this paper, we propose Probabilistic discrete-time Projection Temporal Logic (PrPTL), which extends Projection Temporal Logic (PTL) with probability. To this end, some useful formulas are derived and some logic laws are given. Further,…
We present an efficient algorithm to reduce the size of nondeterministic Buchi word automata, while retaining their language. Additionally, we describe methods to solve PSPACE-complete automata problems like universality, equivalence and…
Deep neural networks, (DNNs, a.k.a. NNs), have been widely used in various tasks and have been proven to be successful. However, the accompanied expensive computing and storage costs make the deployments in resource-constrained devices a…
Finite linear temporal logic ($\mathsf{LTL}_f$) is a powerful formal representation for modeling temporal sequences. We address the problem of learning a compact $\mathsf{LTL}_f$ formula from labeled traces of system behavior. We propose a…
Timed Automata (TA) is de facto a standard modelling formalism to represent systems when the interest is the analysis of their behaviour as time progresses. This modelling formalism is mostly used for checking whether the behaviours of a…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
In a previous work Baillot and Terui introduced Dual light affine logic (DLAL) as a variant of Light linear logic suitable for guaranteeing complexity properties on lambda calculus terms: all typable terms can be evaluated in polynomial…
We consider the problem of explaining the temporal behavior of black-box systems using human-interpretable models. To this end, based on recent research trends, we rely on the fundamental yet interpretable models of deterministic finite…