Exercise on determinizing and minimizing an automaton.

4 files changed, 95 insertions, 0 deletions

diff --git a/figs/ex1p2a.dot b/figs/ex1p2a.dot
new file mode 100644
index 0000000..41870a1
--- /dev/null
+++ b/figs/ex1p2a.dot
@@ -0,0 +1,23 @@
+digraph ex1p2a {
+	rankdir="LR";
+	node [texmode="math",shape="circle",style="state"];
+	q0 [style="state,initial",label="0"];
+	q1 [style="state",label="1"];
+	q2 [style="state",label="2"];
+	q3 [style="state",label="3"];
+	q4 [style="state",label="4"];
+	q5 [style="state",label="5"];
+	q6 [style="state",label="6"];
+	q7 [style="state,final",label="7"];
+	edge [texmode="math",lblstyle="auto"];
+	q0 -> q0 [label="a,b",topath="loop below"];
+	q0 -> q1 [label="e",texlbl="$\varepsilon$"];
+	q0 -> q4 [label="e",texlbl="$\varepsilon$"];
+	q1 -> q2 [label="a"];
+	q4 -> q5 [label="b"];
+	q2 -> q3 [label="a"];
+	q5 -> q6 [label="b"];
+	q3 -> q7 [label="e",texlbl="$\varepsilon$"];
+	q6 -> q7 [label="e",texlbl="$\varepsilon$"];
+	q7 -> q7 [label="a,b",topath="loop below"];
+}
diff --git a/figs/ex1p2b.dot b/figs/ex1p2b.dot
new file mode 100644
index 0000000..34ed531
--- /dev/null
+++ b/figs/ex1p2b.dot
@@ -0,0 +1,19 @@
+digraph ex1p2b {
+	rankdir="LR";
+	node [texmode="math",shape="circle",style="state"];
+	q0 [style="state,initial",label="0"];
+	q2 [style="state",label="2"];
+	q3 [style="state,final,accepting above",label="3"];
+	q5 [style="state",label="5"];
+	q6 [style="state,final,accepting below",label="6"];
+	q7 [style="state,final",label="7"];
+	edge [texmode="math",lblstyle="auto"];
+	q0 -> q0 [label="a,b",topath="loop below"];
+	q0 -> q2 [label="a"];
+	q0 -> q5 [label="b"];
+	q2 -> q3 [label="a"];
+	q5 -> q6 [label="b"];
+	q3 -> q7 [label="a,b"];
+	q6 -> q7 [label="a,b"];
+	q7 -> q7 [label="a,b",topath="loop below"];
+}
diff --git a/figs/ex1p2c.dot b/figs/ex1p2c.dot
new file mode 100644
index 0000000..84317c1
--- /dev/null
+++ b/figs/ex1p2c.dot
@@ -0,0 +1,36 @@
+digraph ex1p2c {
+	rankdir="LR";
+	node [texmode="math",shape="circle",style="state"];
+	q0 [style="state,initial",label="0"];
+	q05 [style="state",label="05"];
+	q056 [style="state,final,accepting below",label="056"];
+	q02 [style="state",label="02"];
+	q023 [style="state,final,accepting above",label="023"];
+	q057 [style="state,final",label="057"];
+	q0567 [style="state,final,accepting above",label="0567"];
+	q027 [style="state,final",label="027"];
+	q0237 [style="state,final,accepting below",label="0237"];
+	edge [texmode="math",lblstyle="auto"];
+	q0 -> q05 [label="b"];
+	q0 -> q02 [label="a"];
+	q05 -> q02 [label="a"];
+	q02 -> q05 [label="b"];
+	{ rank="same"; q05; q02; }
+	q05 -> q056 [label="b"];
+	q02 -> q023 [label="a"];
+	q056 -> q0567 [label="b"];
+	q056 -> q027 [label="a"];
+	q023 -> q0237 [label="a"];
+	q023 -> q057 [label="b"];
+	{ rank="same"; q056; q023; }
+	q0567 -> q027 [label="a",lblstyle="auto,below"];
+	q027 -> q057 [label="b"];
+	q057 -> q0237 [label="a"];
+	q0237 -> q057 [label="b"];
+	q057 -> q027 [label="a"];
+	q027 -> q0567 [label="b",lblstyle="auto,above"];
+	{ rank="same"; q057; q027; }
+	{ rank="same"; q0567; q0237; }
+	q0237 -> q0237 [label="a",topath="loop above"];
+	q0567 -> q0567 [label="b",topath="loop below"];
+}
diff --git a/figs/ex1p2d.dot b/figs/ex1p2d.dot
new file mode 100644
index 0000000..7dd540c
--- /dev/null
+++ b/figs/ex1p2d.dot
@@ -0,0 +1,17 @@
+digraph ex1p2d {
+	rankdir="LR";
+	node [texmode="math",shape="circle",style="state"];
+	q0 [style="state,initial",label="0"];
+	q05 [style="state",label="05"];
+	q02 [style="state",label="02"];
+	qA [style="state,final",label="A"];
+	edge [texmode="math",lblstyle="auto"];
+	q0 -> q05 [label="b"];
+	q0 -> q02 [label="a"];
+	q05 -> q02 [label="a"];
+	q02 -> q05 [label="b"];
+	{ rank="same"; q05; q02; }
+	q05 -> qA [label="b",lblstyle="auto,below"];
+	q02 -> qA [label="a"];
+	qA -> qA [label="a,b",topath="loop below"];
+}