This is the errata page for my book published in 2004
My thanks to the Japanese translator, Ryoma Sin'ya of Akita University,
for alerting me to the typos he has found in the course of his translation work.
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Page X.
"Chapter~2, omitting Section~2.5, can be regarded as a collection of examples.” should read "Chapter~2, omitting Section~2.6, can be regarded as a collection of examples.” |
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Page 5. Exercise 1.1.1.
It is better to use Italic font style for denoting aardvark. |
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Page 13. Example 1.4.1.
The sentence “HH and input the string aba Then” should read “HH and input the string aba, then” |
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Page 39. Example 2.4.4.
The last sentence: "It is now easy to draw the transition table of the required automaton” Transition table should read transition diagram. |
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Page 43. Proof of Proposition
2.5.5.
"But this is equivalent to s0 ·x
∈ F and t0 ·x ∈ G,” The word `and' should be be
emphasised.
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Page 71. Proof of Proposition
3.3.6.
"the strings u_1, (a_1u_2), . .
. , (a_{n−1} u_n) is accepted by L(A)”
should read "the strings u_1,
(a_1u_2), . . . , (a_{n−1} u_n) is accepted by A”
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Page 72. The 4th equation of
Section 3.4.
“L(A) = I \cdot A^* \cap T \neq
\emptyset” should read “L(A) = \{ w \in A^* \mid I
\cdot w \cap T \neq \emptyset \}"
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Page 89. Example 4.1.3.
“We calculate $\A$ for the
$\id$-automaton of …” should read “We calculate
$\A^s$ for the $\id$-automaton of …”
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Page 92. The last sentence of
the proof of Theorem 4.2.1.
“It is easy to check that
$L({\bf B}) = L$” should read “It is easy to check
that $L({\bf D}) = L$”
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Page 115. The second line.
"where $b$ and $c$ are known”
should read "where $a$, $b$ and $c$ are known”
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Page 123 (middle). In the proof of
Theorem 5.4.9.
"By using the ith row of the
equation X = CX + R,” should read "By using the ith
row of the equation X' = C’X' + R’,"
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Page 133. Example 6.1.7.
“given by the transition table
below:” should read “given by the transition diagram
below:”
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Page 135. In the proof of
Theorem 6.2.1-(1).
"Finally, the set of terminal
states is defined to be $T$” should read
"Finally, the set of terminal states is defined to
be $T = T_1 \cup T_2$”
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Page 137. The definition
of $F(r)$.
$F(r) = \{x \in A^{2} \colon \:
A^{\ast} \cap L(r) \neq \emptyset \}$ should read
$F(r) = \{x \in A^{2} \colon \: A^{\ast} x A^{\ast}
\cap L(r) \neq \emptyset \}$
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Page 141, line 6. "As we shall
prove later in this section,’ should read "As
we shall prove later in this chapter,"
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Page 150, Theorem 7. Forgot a
fullstop in the statement.
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Page 155, in the proof of
Theorem 7.4.2. "Now B is reduced,” should read “Now
A and B are reduced,”
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Page 163, Example 7.5.10, Item
(7). "By Proposition 7.5.4” should read “By
Proposition 7.5.3”
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Page 168, Summary of Chapter 7,
about minimal automata. “reduced and connected”
should read “reduced and accessible”
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Page 181, Algorithm 8.2.5. "By
construction, $| vw’ | < |w|$”. This is not true
because a relation can have words with same length.
“By construction, for the tree order $<$, $ vw’
< w $” is ok.
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Page 192, Example 9.1.2. Forgot
fullstop before “Here”.
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Page 201, Example 9.2.5.
"Proposition 9.2.4” should read “Theorem 9.2.4”
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Page 206, 1st line (Example
9.2.14). There is missing notation here.
$\mathbb{Z}_{n}$ should be formally defined.
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Page 209, in the proof of
Theorem 9.4.1. “Then $ i \cdot (uxv) \in L $” should
read “Then $ i \cdot (uxv) \in T $"
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Page 214, Remarks on Chapter 9,
1st paragraph. The relation $\rho_\A$ is written as
$\rho$ twice.
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Page 218, proof of Theorem
10.1.2. "$i, i+1, \ldots i +
(k-1)$" -> "$i, i+1, \ldots, i + (k-1)$”
(forgot a comma before $i+(k-1)$).
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Page 222, 1st paragraph.
"$\pi_{1}, \pi_{2} \colon \: S \times T \rightarrow
S$” should read "$\pi_{1} \colon \: S \times T
\rightarrow S, \pi_{2} \colon \: S \times
T \rightarrow T$”
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Page
222, Example 10.1.9. “Let
$S_{1},S_{3},S_{3}$” should read “Let
$S_{1},S_{2},S_{3}$”.
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Page
230, proof of Proposition 10.2.11. "be
monoid homomorphisms such that and $L_{1} =
\alpha_{1}^{-1}(P_{1})$ and $L_{2} =
\alpha_{2}^{-1}(P_{2})$.”should read “be monoid
homomorphisms such that $L_{1} =
\alpha_{1}^{-1}(P_{1})$ and $L_{2} =
\alpha_{2}^{-1}(P_{2})$ holds for some
subsets \(P_{1} \subseteq M_{1}\) and \(P_{2}
\subseteq M_{2}\)."
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Page
253, proof of Theorem 11.4.2. "If $r = s'$ then
$L(s)$ recognises $s'$ by Proposition~10.2.8(i);
in fact, in this case
$L(s)$ is also the syntactic monoid of $s’$.” should
read "If $r = s'$ then $M$ recognises $L(s’)$ by
Proposition~10.2.8(i);”
in
fact, in this case $M$ is also
the syntactic monoid of $L(s’)$."
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Page
257, proof of Proposition 11.4.9, the last
sentence. "Thus $\phi (u) = n \phi(a)$,
where $n \phi(a)M = mM$. Thus $n = \phi (w) =
\phi(u)\phi(v) = n \phi(a)\phi(v) \in mM$.”
should read “Thus $\phi (u) = n' \phi(a)$, where $n'
\phi(a)M = mM$ for some $n’ \in M$ and $a \in A$. Thus $n = \phi
(w) = \phi(u)\phi(v) = n' \phi(a)\phi(v) \in mM$.”
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Page 260, the last equation.
Forgotten a fullstop.
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Page 267, Examples 12.1.3-(4).
"The proof of (VM2) follows from Lemma~11.2.13,”
should read "The proof of (VM2) follows from
Lemma~11.2.5,”.
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Page 270, after proof of
Lemma 12.1.8. "The definition below is not an
obvious one, although it is partially motivated by
Lemma~12.1.7.”
should read "The
definition below is not an obvious one, although it
is partially motivated by Lemma~12.1.8.”
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Page 274, first sentence. "We
shall now describe a method for describing
pseudovarieties of semigroups.” should read "We
shall now describe a method for describing
pseudovarieties of monoids” (pseudovariety of
semigroups has not yet been defined).
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Page 274, before Example 12.2.3.
The notion “ultimately defined” has yet to have
been defined. Thus add the following sentence after
the definition of $\mathsf{M}’’$: “We say that
$\mathsf{M}''$ is {\em ultimately defined} by the
equations $(u_{n} = v_{n})_{n \geq 1}$.”
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Page 274, Example 12.2.3. “By
Theorem 10.3.2,” should read “By Theorem 11.3.2,”
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Page 275, proof of Theorem
12.2.4. "Put $A_{n} = \{a_{1}, \ldots a_{n} \}$.”
should read "Put $A_{n} = \{a_{1}, \ldots, a_{n}
\}$.”
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Page 275, proof of Theorem
12.2.4, second paragraph. $A_n$ is written as $A$
twice.
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Page 276, Remarks on Chapter 12.
"condition (VL1) is natural from
the point of view of the results we proved back in
Section~2.6;” should read "condition (VL1) is
natural from the point of view of the results we
proved back in Section~2.5;”
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