47 lines
1.2 KiB
Python
47 lines
1.2 KiB
Python
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"""Marking — Convert k-OA to SOA over Σ^(k) (Definition 4.4, arXiv 1004.2372)."""
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from .soa import SOA
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from .expr import strip_k
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def mark_koa(G):
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"""
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Mark a k-OA G as a SOA over Σ^(k).
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Process nodes in arbitrary order. For the i-th occurrence of label a,
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replace by a^(i) (represented as "a_i").
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Returns a SOA H over Σ^(k) such that L(G) = strip(L(H)).
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"""
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H = SOA()
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H.src = G.src
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H.sink = G.sink
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H._succ = {n: set(succ) for n, succ in G._succ.items()}
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H._pred = {n: set(pred) for n, pred in G._pred.items()}
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H._label = {}
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H._next = G._next
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counts = {}
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for n in G._succ:
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lab = G._label.get(n)
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if lab and lab not in ('ε', '∅') and n not in (G.src, G.sink):
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sym = strip_k(lab)
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counts[sym] = counts.get(sym, 0) + 1
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H._label[n] = f"{sym}_{counts[sym]}"
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elif n in (G.src, G.sink):
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H._label[n] = None
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else:
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H._label[n] = lab
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return H
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def strip_expression(expr):
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"""Strip k-ORE markers from expression: a_i → a.
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Returns expression over original alphabet Σ.
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"""
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import re
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result = re.sub(r'(_\d+)', '', expr)
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return result
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