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In this paper we analyze some intrusion detection strategies proposed in the literature and we show that they represent the various facets of a well known formal languages problem: computing the distance between a string and a language . In particular, the main differences among the various approaches adopted for building intrusion detection systems can be reduced to the characteristics of the language and to the notion of distance adopted. As a further contribution we will also show that from...

We investigate the possibility of extending Chrobak normal form to the probabilistic case. While in the nondeterministic case a unary automaton can be simulated by an automaton in Chrobak normal form without increasing the number of the states in the cycles, we show that in the probabilistic case the simulation is not possible by keeping the same number of ergodic states. This negative result is proved by considering the natural extension to the probabilistic case of Chrobak normal form, obtained...

We investigate the possibility of extending Chrobak normal form to the probabilistic case. While in the nondeterministic case a unary automaton can be simulated by an automaton in Chrobak normal form without increasing the number of the states in the cycles, we show that in the probabilistic case the simulation is not possible by keeping the same number of ergodic states. This negative result is proved by considering the natural extension to the...

We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family $\left\{L_m\right\}$ of cyclic languages, where $L_m=\left\{a^{km}\right|k\in \mathbb{N}\}$. In particular, we show that, for any $m$, the number of states necessary and sufficient for accepting the unary language $L_m$ with isolated cut point on one-way probabilistic finite automata is $p_1^{{\alpha }_1}+p_2^{{\alpha }_2}+\cdots +p_s^{{\alpha }_s}$, with $p_1^{{\alpha }_1}{p}_2^{{\alpha }_2}\cdots p_s^{{\alpha }_s}$ being the factorization of $m$. To prove this result, we give a general state lower bound for accepting unary languages with isolated cut point on...

We investigate the possibility of extending Chrobak normal form to the probabilistic case. While in the nondeterministic case a unary automaton can be simulated by an automaton in Chrobak normal form without increasing the number of the states in the cycles, we show that in the probabilistic case the simulation is not possible by keeping the same number of ergodic states. This negative result is proved by considering the natural extension to the...

We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {} of cyclic languages, where = | ∈ . In particular, we show that, for any , the number of states necessary and sufficient for accepting the unary language with isolated cut point on one-way probabilistic finite automata is $p_1^{{\alpha }_1}+p_2^{{\alpha }_2}+\cdots +p_s^{{\alpha }_s}$, with $p_1^{{\alpha }_1}{p}_2^{{\alpha }_2}\cdots p_s^{{\alpha }_s}$ being the factorization of . To prove this result, we give a Moreover, we exhibit one-way quantum finite automata...