We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given k-automatic sequence is ultimately periodic. We prove

Given an n-state unary finite automaton accepting a language T , and an ultimately periodic set S given as a union of arithmetic progressions that can be represented using n bits, and whose periods are mutually coprime, deciding whether T ⊆ S is in n n) time. Dropping the mutual coprimality condition, this containment problem becomes NP-hard.

We examine the dynamics of multiple reinforcement learning agents who are interacting with and learning from the same environment in parallel. Due to the stochasticity of the environment, each agent will have a different learning experience though they should all ultimately converge upon the same value function. The agents can accelerate the learning process by sharing information at periodic p...

This article is concerned with the ultimately bounded filtering problem for a class of linear time-delay systems subject to norm-bounded disturbances and impulsive measurement outliers (IMOs). The considered IMOs are modeled by sequence signals certain known minimum norm (i.e., norms all signals). In order characterize occasional occurrence IMOs, independent identically distributed random varia...

The A5/1 algorithm is one of the most famous stream cipher algorithms used for over-the-air communication privacy in GSM. The purpose of this paper is to analyze several weaknesses of A5/1, including an improvement to an attack and investigation of the A5/1 state transition. Biham and Dunkelman proposed an attack on A5/1 with a time and data complexity of 239.91and 221.1, ...