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Reactive synthesis is the task of automatically deriving a correct implementation from a specification. It is a promising technique for the development of verified programs and hardware. Despite recent advances in terms of algorithms and…

Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…

Simultaneous decompositions of a pair of states into pure ones are examined. There are privileged decompositions which are distinguished from all the other ones.

The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…

Classical approaches like process algebras or labelled transition systems deal with static composition to model non-trivial concurrent or distributed systems; this is not sufficient for systems with dynamic architecture and with variable…

Explanation generation frameworks aim to make AI systems' decisions transparent and understandable to human users. However, generating explanations in uncertain environments characterized by incomplete information and probabilistic models…

Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…

We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…

We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decompo- sition has multiple applications. In some concrete cases, we use it to construct…

A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…

Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…

Decomposition of text into atomic propositions is a flexible framework allowing for the closer inspection of input and output text. We use atomic decomposition of hypotheses in two natural language reasoning tasks, traditional NLI and…

To account for phenomenological theories and a set of invariants, stress and strain are usually decomposed into a pair of pressure and deviatoric stress and a pair of volumetric strain and deviatoric strain. However, the conventional…

This paper presents an integer decomposition method. The method first writes an integer as a polynomial with 2 as variable that its coefficients are zero or one. Then, suppose that an integer is decomposed into product of such two…

A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete…

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…

This paper constructs a foundation to analyze semi-group actions, group actions, filtrations, and decompositions in a unified manner. In fact, though the studies of decomposition can be applied to foliated spaces and group actions, they can…

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…

We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results we give an algorithm for the following problem: given a homogeneous polynomial of degree 3, decide whether it can be…

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…