We present an on-line linear time and space algorithm to check if an integer array $f$ is the border array of at least one string $w$ built on a bounded or unbounded size alphabet $\Sigma$. First of all, we show a bijection between the border array of a string $w$ and the skeleton of the DFA recognizing ${\Sigma }^{*}w$, called a string matching automaton (SMA). Different strings can have the same border array but the originality of the presented method is that the correspondence between a border array and a skeleton of SMA...

We present an on-line linear time and space algorithm to check if an integer array f is the border array of at least one string w built on a bounded or unbounded size alphabet Σ. First of all, we show a bijection between the border array of a string w and the skeleton of the DFA recognizing Σ*ω, called a string matching automaton (SMA). Different strings can have the same border array but the originality of the presented method is that the correspondence between a border array and a...

This paper considers a distributed aggregative game problem for a group of players with misinformation, where each player has a different perception of the game. Player’s deception behavior is inevitable in this situation for reducing its own cost. We utilize hypergame to model the above problems and adopt $ϵ$-Nash equilibrium for hypergame to investigate whether players believe in their own cognition. Additionally, we propose a distributed deceptive algorithm for a player implementing deception and...