Related papers: Decompositions and complexity of linear automata
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…
We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs. The dioid structure of the set of costs allows for…
We study the problem of constructing approximations to a weighted automaton. Weighted finite automata (WFA) are closely related to the theory of rational series. A rational series is a function from strings to real numbers that can be…
Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point -- a stationary point of the hyper-objective function obtained by minimizing or maximizing…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…
We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the…
This work investigates the manufacturing of complex shapes parts with wire arc additive manufacturing (WAAM). In order to guarantee the integrity and quality of each deposited layer that composes the final piece, the deposition process is…
Opacity is an information flow property characterizing whether a system reveals its secret to an intruder. Verification of opacity for discrete-event systems modeled by automata is in general a hard problem. We discuss the question whether…
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…
We exhibit an algorithm with continuous instructions for two robots moving without collisions on a track shaped as a wedge of three circles. We show that the topological complexity of the configuration space associated with this problem is…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…
Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…
Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations…
A three-way (resp., two-way) two-dimensional automaton has a read-only input head that moves in three (resp., two) directions on a finite array of cells labelled by symbols of the input alphabet. Restricting the input head movement of a…
We give a new, and hopefully more easily understandable, structural proof of the decomposition of a $k$-valued transducer into $k$ unambiguous functional ones, a result established by A. Weber in 1996. Our construction is based on a…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…