1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
|
// properties.cc
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Copyright 2005-2010 Google, Inc.
// Author: riley@google.com (Michael Riley)
//
// \file
// Functions for updating property bits for various FST operations and
// string names of the properties.
#include <fst/properties.h>
#include <stddef.h>
#include <vector>
using std::vector;
namespace fst {
// These functions determine the properties associated with the FST
// result of various finite-state operations. The property arguments
// correspond to the operation's FST arguments. The properties
// returned assume the operation modifies its first argument.
// Bitwise-and this result with kCopyProperties for the case when a
// new (possibly delayed) FST is instead constructed.
// Properties for a concatenatively-closed FST.
uint64 ClosureProperties(uint64 inprops, bool star, bool delayed) {
uint64 outprops = (kError | kAcceptor | kUnweighted | kAccessible) & inprops;
if (!delayed)
outprops |= (kExpanded | kMutable | kCoAccessible |
kNotTopSorted | kNotString) & inprops;
if (!delayed || inprops & kAccessible)
outprops |= (kNotAcceptor | kNonIDeterministic | kNonODeterministic |
kNotILabelSorted | kNotOLabelSorted | kWeighted |
kNotAccessible | kNotCoAccessible) & inprops;
return outprops;
}
// Properties for a complemented FST.
uint64 ComplementProperties(uint64 inprops) {
uint64 outprops = kAcceptor | kUnweighted | kNoEpsilons |
kNoIEpsilons | kNoOEpsilons |
kIDeterministic | kODeterministic | kAccessible;
outprops |= (kError | kILabelSorted | kOLabelSorted | kInitialCyclic) &
inprops;
if (inprops & kAccessible)
outprops |= kNotILabelSorted | kNotOLabelSorted | kCyclic;
return outprops;
}
// Properties for a composed FST.
uint64 ComposeProperties(uint64 inprops1, uint64 inprops2) {
uint64 outprops = kError & (inprops1 | inprops2);
if (inprops1 & kAcceptor && inprops2 & kAcceptor) {
outprops |= kAcceptor | kAccessible;
outprops |= (kNoEpsilons | kNoIEpsilons | kNoOEpsilons | kAcyclic |
kInitialAcyclic) & inprops1 & inprops2;
if (kNoIEpsilons & inprops1 & inprops2)
outprops |= (kIDeterministic | kODeterministic) & inprops1 & inprops2;
} else {
outprops |= kAccessible;
outprops |= (kAcceptor | kNoIEpsilons | kAcyclic | kInitialAcyclic) &
inprops1 & inprops2;
if (kNoIEpsilons & inprops1 & inprops2)
outprops |= kIDeterministic & inprops1 & inprops2;
}
return outprops;
}
// Properties for a concatenated FST.
uint64 ConcatProperties(uint64 inprops1, uint64 inprops2, bool delayed) {
uint64 outprops =
(kAcceptor | kUnweighted | kAcyclic) & inprops1 & inprops2;
outprops |= kError & (inprops1 | inprops2);
bool empty1 = delayed; // Can fst1 be the empty machine?
bool empty2 = delayed; // Can fst2 be the empty machine?
if (!delayed) {
outprops |= (kExpanded | kMutable | kNotTopSorted | kNotString) & inprops1;
outprops |= (kNotTopSorted | kNotString) & inprops2;
}
if (!empty1)
outprops |= (kInitialAcyclic | kInitialCyclic) & inprops1;
if (!delayed || inprops1 & kAccessible)
outprops |= (kNotAcceptor | kNonIDeterministic | kNonODeterministic |
kEpsilons | kIEpsilons | kOEpsilons | kNotILabelSorted |
kNotOLabelSorted | kWeighted | kCyclic |
kNotAccessible | kNotCoAccessible) & inprops1;
if ((inprops1 & (kAccessible | kCoAccessible)) ==
(kAccessible | kCoAccessible) && !empty1) {
outprops |= kAccessible & inprops2;
if (!empty2)
outprops |= kCoAccessible & inprops2;
if (!delayed || inprops2 & kAccessible)
outprops |= (kNotAcceptor | kNonIDeterministic | kNonODeterministic |
kEpsilons | kIEpsilons | kOEpsilons | kNotILabelSorted |
kNotOLabelSorted | kWeighted | kCyclic |
kNotAccessible | kNotCoAccessible) & inprops2;
}
return outprops;
}
// Properties for a determinized FST.
uint64 DeterminizeProperties(uint64 inprops, bool has_subsequential_label) {
uint64 outprops = kAccessible;
if (((kAcceptor | kNoIEpsilons) & inprops) || has_subsequential_label)
outprops |= kIDeterministic;
outprops |= (kError | kAcceptor | kAcyclic |
kInitialAcyclic | kCoAccessible | kString) & inprops;
if (inprops & kNoIEpsilons)
outprops |= kNoEpsilons & inprops;
if (inprops & kAccessible)
outprops |= (kNotAcceptor | kEpsilons | kIEpsilons | kOEpsilons |
kCyclic) & inprops;
if (inprops & kAcceptor)
outprops |= (kNoIEpsilons | kNoOEpsilons) & inprops;
if ((inprops & kNoIEpsilons) && has_subsequential_label)
outprops |= kNoIEpsilons;
return outprops;
}
// Properties for factored weight FST.
uint64 FactorWeightProperties(uint64 inprops) {
uint64 outprops = (kExpanded | kMutable | kError | kAcceptor |
kAcyclic | kAccessible | kCoAccessible) & inprops;
if (inprops & kAccessible)
outprops |= (kNotAcceptor | kNonIDeterministic | kNonODeterministic |
kEpsilons | kIEpsilons | kOEpsilons | kCyclic |
kNotILabelSorted | kNotOLabelSorted)
& inprops;
return outprops;
}
// Properties for an inverted FST.
uint64 InvertProperties(uint64 inprops) {
uint64 outprops = (kExpanded | kMutable | kError | kAcceptor | kNotAcceptor |
kEpsilons | kNoEpsilons | kWeighted | kUnweighted |
kCyclic | kAcyclic | kInitialCyclic | kInitialAcyclic |
kTopSorted | kNotTopSorted |
kAccessible | kNotAccessible |
kCoAccessible | kNotCoAccessible |
kString | kNotString) & inprops;
if (kIDeterministic & inprops)
outprops |= kODeterministic;
if (kNonIDeterministic & inprops)
outprops |= kNonODeterministic;
if (kODeterministic & inprops)
outprops |= kIDeterministic;
if (kNonODeterministic & inprops)
outprops |= kNonIDeterministic;
if (kIEpsilons & inprops)
outprops |= kOEpsilons;
if (kNoIEpsilons & inprops)
outprops |= kNoOEpsilons;
if (kOEpsilons & inprops)
outprops |= kIEpsilons;
if (kNoOEpsilons & inprops)
outprops |= kNoIEpsilons;
if (kILabelSorted & inprops)
outprops |= kOLabelSorted;
if (kNotILabelSorted & inprops)
outprops |= kNotOLabelSorted;
if (kOLabelSorted & inprops)
outprops |= kILabelSorted;
if (kNotOLabelSorted & inprops)
outprops |= kNotILabelSorted;
return outprops;
}
// Properties for a projected FST.
uint64 ProjectProperties(uint64 inprops, bool project_input) {
uint64 outprops = kAcceptor;
outprops |= (kExpanded | kMutable | kError | kWeighted | kUnweighted |
kCyclic | kAcyclic | kInitialCyclic | kInitialAcyclic |
kTopSorted | kNotTopSorted | kAccessible | kNotAccessible |
kCoAccessible | kNotCoAccessible |
kString | kNotString) & inprops;
if (project_input) {
outprops |= (kIDeterministic | kNonIDeterministic |
kIEpsilons | kNoIEpsilons |
kILabelSorted | kNotILabelSorted) & inprops;
if (kIDeterministic & inprops)
outprops |= kODeterministic;
if (kNonIDeterministic & inprops)
outprops |= kNonODeterministic;
if (kIEpsilons & inprops)
outprops |= kOEpsilons | kEpsilons;
if (kNoIEpsilons & inprops)
outprops |= kNoOEpsilons | kNoEpsilons;
if (kILabelSorted & inprops)
outprops |= kOLabelSorted;
if (kNotILabelSorted & inprops)
outprops |= kNotOLabelSorted;
} else {
outprops |= (kODeterministic | kNonODeterministic |
kOEpsilons | kNoOEpsilons |
kOLabelSorted | kNotOLabelSorted) & inprops;
if (kODeterministic & inprops)
outprops |= kIDeterministic;
if (kNonODeterministic & inprops)
outprops |= kNonIDeterministic;
if (kOEpsilons & inprops)
outprops |= kIEpsilons | kEpsilons;
if (kNoOEpsilons & inprops)
outprops |= kNoIEpsilons | kNoEpsilons;
if (kOLabelSorted & inprops)
outprops |= kILabelSorted;
if (kNotOLabelSorted & inprops)
outprops |= kNotILabelSorted;
}
return outprops;
}
// Properties for a randgen FST.
uint64 RandGenProperties(uint64 inprops, bool weighted) {
uint64 outprops = kAcyclic | kInitialAcyclic | kAccessible;
outprops |= inprops & kError;
if (weighted) {
outprops |= kTopSorted;
outprops |= (kAcceptor | kNoEpsilons |
kNoIEpsilons | kNoOEpsilons |
kIDeterministic | kODeterministic |
kILabelSorted | kOLabelSorted) & inprops;
} else {
outprops |= kUnweighted;
outprops |= (kAcceptor | kILabelSorted | kOLabelSorted) & inprops;
}
return outprops;
}
// Properties for a replace FST.
uint64 ReplaceProperties(const vector<uint64>& inprops,
ssize_t root,
bool epsilon_on_replace,
bool no_empty_fsts) {
if (inprops.size() == 0)
return kNullProperties;
uint64 outprops = 0;
for (size_t i = 0; i < inprops.size(); ++i)
outprops |= kError & inprops[i];
uint64 access_props = no_empty_fsts ? kAccessible | kCoAccessible : 0;
for (size_t i = 0; i < inprops.size(); ++i)
access_props &= (inprops[i] & (kAccessible | kCoAccessible));
if (access_props == (kAccessible | kCoAccessible)) {
outprops |= access_props;
if (inprops[root] & kInitialCyclic)
outprops |= kInitialCyclic;
uint64 props = 0;
bool string = true;
for (size_t i = 0; i < inprops.size(); ++i) {
if (epsilon_on_replace == false)
props |= kNotAcceptor & inprops[i];
props |= (kNonIDeterministic | kNonODeterministic | kEpsilons |
kIEpsilons | kOEpsilons | kWeighted | kCyclic |
kNotTopSorted | kNotString) & inprops[i];
if (!(inprops[i] & kString))
string = false;
}
outprops |= props;
if (string)
outprops |= kString;
}
bool acceptor = epsilon_on_replace;
bool ideterministic = !epsilon_on_replace;
bool no_iepsilons = !epsilon_on_replace;
bool acyclic = true;
bool unweighted = true;
for (size_t i = 0; i < inprops.size(); ++i) {
if (!(inprops[i] & kAcceptor))
acceptor = false;
if (!(inprops[i] & kIDeterministic))
ideterministic = false;
if (!(inprops[i] & kNoIEpsilons))
no_iepsilons = false;
if (!(inprops[i] & kAcyclic))
acyclic = false;
if (!(inprops[i] & kUnweighted))
unweighted = false;
}
if (acceptor)
outprops |= kAcceptor;
if (ideterministic)
outprops |= kIDeterministic;
if (no_iepsilons)
outprops |= kNoIEpsilons;
if (acyclic)
outprops |= kAcyclic;
if (unweighted)
outprops |= kUnweighted;
if (inprops[root] & kInitialAcyclic)
outprops |= kInitialAcyclic;
return outprops;
}
// Properties for a relabeled FST.
uint64 RelabelProperties(uint64 inprops) {
uint64 outprops = (kExpanded | kMutable | kError |
kWeighted | kUnweighted |
kCyclic | kAcyclic |
kInitialCyclic | kInitialAcyclic |
kTopSorted | kNotTopSorted |
kAccessible | kNotAccessible |
kCoAccessible | kNotCoAccessible |
kString | kNotString) & inprops;
return outprops;
}
// Properties for a reversed FST. (the superinitial state limits this set)
uint64 ReverseProperties(uint64 inprops) {
uint64 outprops =
(kExpanded | kMutable | kError | kAcceptor | kNotAcceptor | kEpsilons |
kIEpsilons | kOEpsilons | kWeighted | kUnweighted |
kCyclic | kAcyclic) & inprops;
return outprops;
}
// Properties for re-weighted FST.
uint64 ReweightProperties(uint64 inprops) {
uint64 outprops = inprops & kWeightInvariantProperties;
outprops = outprops & ~kCoAccessible;
return outprops;
}
// Properties for an epsilon-removed FST.
uint64 RmEpsilonProperties(uint64 inprops, bool delayed) {
uint64 outprops = kNoEpsilons;
outprops |= (kError | kAcceptor | kAcyclic | kInitialAcyclic) & inprops;
if (inprops & kAcceptor)
outprops |= kNoIEpsilons | kNoOEpsilons;
if (!delayed) {
outprops |= kExpanded | kMutable;
outprops |= kTopSorted & inprops;
}
if (!delayed || inprops & kAccessible)
outprops |= kNotAcceptor & inprops;
return outprops;
}
// Properties for shortest path. This function computes how the properties
// of the output of shortest path need to be updated, given that 'props' is
// already known.
uint64 ShortestPathProperties(uint64 props) {
return props | kAcyclic | kInitialAcyclic | kAccessible | kCoAccessible;
}
// Properties for a synchronized FST.
uint64 SynchronizeProperties(uint64 inprops) {
uint64 outprops = (kError | kAcceptor | kAcyclic | kAccessible |
kCoAccessible | kUnweighted) & inprops;
if (inprops & kAccessible)
outprops |= (kCyclic | kNotCoAccessible | kWeighted) & inprops;
return outprops;
}
// Properties for a unioned FST.
uint64 UnionProperties(uint64 inprops1, uint64 inprops2, bool delayed) {
uint64 outprops = (kAcceptor | kUnweighted | kAcyclic | kAccessible)
& inprops1 & inprops2;
outprops |= kError & (inprops1 | inprops2);
outprops |= kInitialAcyclic;
bool empty1 = delayed; // Can fst1 be the empty machine?
bool empty2 = delayed; // Can fst2 be the empty machine?
if (!delayed) {
outprops |= (kExpanded | kMutable | kNotTopSorted | kNotString) & inprops1;
outprops |= (kNotTopSorted | kNotString) & inprops2;
}
if (!empty1 && !empty2) {
outprops |= kEpsilons | kIEpsilons | kOEpsilons;
outprops |= kCoAccessible & inprops1 & inprops2;
}
// Note kNotCoAccessible does not hold because of kInitialAcyclic opt.
if (!delayed || inprops1 & kAccessible)
outprops |= (kNotAcceptor | kNonIDeterministic | kNonODeterministic |
kEpsilons | kIEpsilons | kOEpsilons | kNotILabelSorted |
kNotOLabelSorted | kWeighted | kCyclic |
kNotAccessible) & inprops1;
if (!delayed || inprops2 & kAccessible)
outprops |= (kNotAcceptor | kNonIDeterministic | kNonODeterministic |
kEpsilons | kIEpsilons | kOEpsilons | kNotILabelSorted |
kNotOLabelSorted | kWeighted | kCyclic |
kNotAccessible | kNotCoAccessible) & inprops2;
return outprops;
}
// Property string names (indexed by bit position).
const char *PropertyNames[] = {
// binary
"expanded", "mutable", "error", "", "", "", "", "",
"", "", "", "", "", "", "", "",
// trinary
"acceptor", "not acceptor",
"input deterministic", "non input deterministic",
"output deterministic", "non output deterministic",
"input/output epsilons", "no input/output epsilons",
"input epsilons", "no input epsilons",
"output epsilons", "no output epsilons",
"input label sorted", "not input label sorted",
"output label sorted", "not output label sorted",
"weighted", "unweighted",
"cyclic", "acyclic",
"cyclic at initial state", "acyclic at initial state",
"top sorted", "not top sorted",
"accessible", "not accessible",
"coaccessible", "not coaccessible",
"string", "not string",
};
} // namespace fst
|
