Related papers: Minimization of Automata
In this paper, we introduce the problem of rewriting finite formal languages using syntactic macros such that the rewriting is minimal in size. We present polynomial-time algorithms to solve variants of this problem and show their…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…
In this paper, we first introduce a lower bound technique for the state complexity of transformations of automata. Namely we suggest first considering the class of full automata in lower bound analysis, and later reducing the size of the…
The classification of complex data usually requires the composition of processing steps. Here, a major challenge is the selection of optimal algorithms for preprocessing and classification (including parameterizations). Nowadays, parts of…
The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
We consider the problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment of jobs to machines, to minimize the expected value of the maximum load over all the machines. For…
A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this…
As the ratio between the rate of computation and rate with which data can be retrieved from various layers of memory continues to deteriorate, a question arises: Will the current best algorithms for computing matrix-matrix multiplication on…
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for…
Automaton learning is a domain in which the target system is inferred by the automaton learning algorithm in the form of an automaton, by synthesizing a finite number of inputs and their corresponding outputs. Automaton learning makes use…
This paper presents and analyzes an incremental algorithm for the construction of Acyclic Non-deterministic Finite-state Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons.…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case.…
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…