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Finite State Automata
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Modeling of symbolic systems: Part I  Vector space representation of probabilistic finite state automata
Modeling of symbolic systems: Part I  Vector space representation of probabilistic finite state automata,Yicheng Wen,Asok Ray,Ishanu Chattopadhyay,Sh
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Modeling of symbolic systems: Part I  Vector space representation of probabilistic finite state automata
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Citations: 1
)
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Yicheng Wen
,
Asok Ray
,
Ishanu Chattopadhyay
,
Shashi Phoha
Published in 2011.
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Citation Context
(1)
...The main contribution of this paper lies in the construction of a family of inner products on the vector space of PFSA [
13
]...
...The technical contents of this second part are built upon the vector space of PFSA, which is reported in the first part [
13
]...
...where Np denotes a partition induced by Nerode equivalence [
13
]...
...Q and all σ ∈ �}. Algorithm 1 in the first part [
13
] has been constructed in the context of the probabilistic Nerode equivalence Np such that a map e H : f A → P + f is surjective...
...By Algorithm 1 in the first part [
13
], it follows that...
...By use of the bijection H and its inverse F (see Algorithm 1 in the first part [
13
]), new vector addition and scalar multiplication operations are introduced on the quotient space A ...
...Definition II.2 (Vector space A ) Let G1, G2 ∈ A and k ∈ R. Then, following the definitions of vector addition ⊕ and scalar multiplication ⊙ in the space of PFSA in the first part [
13
], • The addition operation + : A × A → A is defined as...
...Proof: It follows from the definitions of vector addition ⊕ and scalar multiplication ⊙ in the space of PFSA in the first part [
13
] that (p1 ⊕ p2)(τ x) = p1(τ x)p2(τ x)...
...The following result is generated based on Algorithm 1 in the first part [
13
]...
...Following the definition of a state transition probability matrix in the first part [
13
], a matrix representation of Eq. (18) is obtained as...
...This second part of the twopart paper introduces a family of inner products on the vector space of PFSA that is constructed in the first part [
13
]...
Yicheng Wen
,
et al.
Modeling of symbolic systems: Part II  Hilbert space construction for...
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(
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International Journal of Control  INT J CONTR
, vol. 81, no. 5, pp. 820835, 2008
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Citations
(1)
Modeling of symbolic systems: Part II  Hilbert space construction for model identification and order reduction
(
Citations: 1
)
Yicheng Wen
,
Asok Ray
,
Ishanu Chattopadhyay
,
Shashi Phoha
Published in 2011.