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build: update dependencies
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main.typ

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Original file line numberDiff line numberDiff line change
@@ -1,12 +1,12 @@
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#import "@preview/ilm:1.4.0": *
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#import "@preview/mannot:0.2.1": *
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#import "@preview/ilm:1.4.1": *
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#import "@preview/mannot:0.3.0": *
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#import "@preview/codly:1.2.0": *
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#import "@preview/codly-languages:0.1.1": *
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#import "@preview/codly:1.3.0": *
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#import "@preview/codly-languages:0.1.8": *
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#show: codly-init
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#codly(languages: codly-languages)
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#import "@preview/fletcher:0.5.4" as fletcher: node
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#import "@preview/fletcher:0.5.8" as fletcher: node
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#let diagram = fletcher.diagram.with(node-stroke: .1em)
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#let trans = fletcher.edge.with(marks: "-|>")
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#let state = fletcher.node.with(shape: circle)
@@ -321,7 +321,7 @@ $ delta((q, r), a) = (delta_1(q, a), delta_2(r, a)) $
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只要 $q in Q_1$$r in Q_2$, 该状态即为 $M$ 的接受状态:
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$
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F = mark((F_1 times Q_2), tag: #<f1>) union mark((Q_1 times F_2), tag: #<f2>, color: #blue)
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F = markhl((F_1 times Q_2), tag: #<f1>) union markhl((Q_1 times F_2), tag: #<f2>, color: #blue)
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#annot(<f1>, pos: top)[$M_1$ 的接受状态与 $M_2$ 的任意状态]
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#annot(<f2>, pos: bottom)[$M_1$ 的任意状态与 $M_2$ 的接受状态]
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$
@@ -405,7 +405,7 @@ $
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NFA 的新特性*均与转移有关*, 因此它与 DFA 的五元组定义相似, 唯一的区别在于转移函数:
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$
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delta: Q times Sigma -> mark(cal(P)(Q), tag: #<powerset>) = { R | R subset.eq Q }
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delta: Q times Sigma -> markhl(cal(P)(Q), tag: #<powerset>) = { R | R subset.eq Q }
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#annot(<powerset>, pos: bottom)[$Q$ 的幂集]
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$
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@@ -425,7 +425,7 @@ $
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eNFA 的定义与 NFA 类似, 但转移函数允许 $epsilon$-转移:
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$
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delta: Q times mark(Sigma_epsilon, tag: #<se>) -> cal(P)(Q) = { R | R subset.eq Q }
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delta: Q times markhl(Sigma_epsilon, tag: #<se>) -> cal(P)(Q) = { R | R subset.eq Q }
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#annot(<se>, pos: bottom)[${Sigma union epsilon}$]
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$
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@@ -553,8 +553,8 @@ $M'$ 中的状态 $R$, 用于同时跟踪 $M$ 中的多个状态. \
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因此在进行状态转移的时候, 也需要分别转移 $R$ 中的每个状态:
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$
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delta'(mark(R, tag: #<r>), a) = { q | q in delta(r, a) "for some" r in R}
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#annot(<r>, pos: bottom, yshift: 0.5em)[$R in Q'$]
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delta'(markhl(R, tag: #<r>), a) = { q | q in delta(r, a) "for some" r in R}
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#annot(<r>, pos: bottom, dy: 0.5em)[$R in Q'$]
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$
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NFA 和 DFA 都只有一个起始状态, 但 $M'$ 中的状态是一个集合:

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