From 995b06c4e9617c44429cc4d0ae3d0518384d6471 Mon Sep 17 00:00:00 2001
From: Peter Wu <peter@lekensteyn.nl>
Date: Mon, 16 Jan 2017 04:51:23 +0100
Subject: NFA: initial solution

Python code is not cleaned up, it is working now... Generated LaTeX code
was not positioned correctly, so just use GraphViz then.
---
 nfa/generate-nfa.py | 118 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 118 insertions(+)
 create mode 100755 nfa/generate-nfa.py

(limited to 'nfa/generate-nfa.py')

diff --git a/nfa/generate-nfa.py b/nfa/generate-nfa.py
new file mode 100755
index 0000000..6255bca
--- /dev/null
+++ b/nfa/generate-nfa.py
@@ -0,0 +1,118 @@
+#!/usr/bin/env python
+# Usage:
+#   $0 [number-of-states] | z3 -smt -in
+# Examples:
+#   $0 25
+
+import itertools
+import sys
+
+# Number of steps
+m = 25 if len(sys.argv) <= 1 else int(sys.argv[1])
+
+# all possible strings
+lang = [
+    "aa",
+    "bb",
+    "aba",
+    "baa",
+    "abab",
+    "babb",
+    "bbba",
+]
+
+# sledgehammer approach: specify all bad words
+fulllang = []
+for n in range(1, 4 + 1):
+    fulllang += [
+        "".join(x)
+        for x in itertools.product(*["ab"] * n)
+    ]
+# Remove good words.
+badlang = [word for word in fulllang if word not in lang]
+
+literals = []
+preds = []
+extrafuns = []
+
+# Populate Q = { q0, q1, ..., q_(m-1) } with unique values.
+literals += ["q%d" % i for i in range(m)]
+preds += ["(= q%d %d)" % (i, i) for i in range(m)]
+
+def mks(word_index, letter_index):
+    """Return variable for a state of a word after some transitions."""
+    return "s%d_%d" % (word_index, letter_index)
+
+# Assuming a single initial state (which may or may not be the final state),
+# add states for every letter j in each word i.
+for i, word in enumerate(lang):
+    for j, letter in enumerate(word):
+        v = mks(i, j)
+        literals += [v]
+        # Each of the states must be assigned to any of the states in Q
+        #preds += ["(>= %s 0)" % v, "(< %s %d)" % (v, m)]
+
+# Transition Δ: Q × Σ -> P(Q). For Σ = {a,b}, we assume this range:
+# transitions (0..; 1..2; 0..)
+extrafuns += ["(trans Int Int Int)"]
+# final states F \subset Q
+extrafuns += ["(final Int Bool)"]
+# Require a transition between each letter
+for i, word in enumerate(lang):
+    state_prev = "q0"
+    for j, letter in enumerate(word):
+        state_next = mks(i, j)
+        label = "ab".index(letter)
+        preds += ["(= (trans %s %d) %s)" % (state_prev, label, state_next)]
+        state_prev = state_next
+    preds += ["(final %s)" % state_prev]
+
+# "a" and "b" are not allowed to accept (length 1)
+#preds += ["(not (final (trans q0 %d)))" % label for label in range(2)]
+for i, word in enumerate(badlang):
+    state_prev = "q0"
+    move = "q0"
+    preconds = []
+    for j, letter in enumerate(word):
+        label = "ab".index(letter)
+        move = "(trans %s %d)" % (move, label)
+        # Ensure result is within range.
+        preconds += ["(>= %s 0)" % move, "(< %s %d)" % (move, m)]
+    preds += ["(=> (and %s) (not (final %s)))" % (" ".join(preconds), move)]
+    #preds += ["(not (final %s))" % move]
+    #valid = "(>= {move} 0) (< {move} {m})".format(**vars())
+    #preds += ["(=> (and %s) (not (final %s)))" % (valid, move)]
+
+# Try to fit any of the letter states with any state from Q
+for i, word in enumerate(lang):
+    for j, letter in enumerate(word):
+        alts = []
+        for qi in range(m):
+            state = "q%d" % qi
+            alts += ["(= %s %s)" % (state, mks(i, j))]
+        preds += ["(or %s)" % " ".join(alts)]
+
+# Begin generator
+s = """(benchmark test.smt
+:logic QF_UFLIA
+:extrafuns (
+"""
+s += "\n".join("(%s Int)" % x for x in literals)
+s += "\n" + "\n".join(extrafuns)
+s += """
+)
+:formula (and
+"""
+s += "\n".join(preds)
+s += """
+))
+"""
+
+try:
+    import sys
+    print(s)
+    # Hack to avoid printing a ugly error in case stdin of next pipe is closed.
+    sys.stdout.flush()
+    sys.stdout.close()
+except BrokenPipeError:
+    pass
-- 
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