Worked on sep seqs.

content/esm.table

@@ -0,0 +1,137 @@
+states	Hopcroft	Moore
+546	0.05548176	0.05162218
+547	0.065968448	0.374567635
+571	0.151784094	2.562025297
+610	0.161709531	2.923059564
+612	0.162847423	2.949833339
+616	0.16393522	2.979295117
+634	0.169730862	3.136451995
+644	0.171697908	3.205603966
+646	0.173519053	3.247711454
+664	0.174829094	3.303879469
+674	0.176219619	3.404398614
+704	0.18026932	3.772591464
+723	0.176796323	4.025279554
+724	0.176144222	4.041852225
+727	0.177380196	4.078740205
+750	0.184511916	4.376803632
+752	0.184925295	4.39675801
+755	0.18608039	4.427337413
+779	0.191979151	4.696313345
+796	0.19801254	4.906009044
+808	0.199559131	4.969958634
+816	0.202306127	5.06486171
+820	0.203567904	5.11139433
+826	0.206071634	5.194849765
+849	0.217511686	5.553222482
+851	0.220003201	5.5797187
+881	0.226420016	5.94774453
+951	0.235091864	6.33370116
+952	0.234470623	6.357592105
+976	0.243413677	6.785026456
+998	0.247111407	7.115376566
+1022	0.254264636	7.475588529
+1028	0.253825238	7.676966117
+1031	0.253552779	7.655207879
+1032	0.253959583	7.687817395
+1036	0.256927602	7.753280811
+1038	0.256454243	7.785150879
+1044	0.2676729	7.914658705
+1048	0.268592945	7.993362548
+1090	0.280256629	8.571307839
+1096	0.283057389	8.72110485
+1104	0.285299766	8.860082549
+1172	0.30334844	9.682438227
+1182	0.308970132	9.785819737
+1222	0.323826492	10.508031711
+1230	0.325670362	10.670810609
+1242	0.331428484	10.796530463
+1248	0.32975737	10.897072507
+1262	0.33353854	11.303006909
+1268	0.338205563	11.351776371
+1460	0.371807782	13.490904423
+1466	0.372692439	13.528562317
+1486	0.380183351	14.004736754
+1492	0.382841945	14.188868672
+1495	0.382159405	14.265695125
+1513	0.388669725	14.900034072
+1516	0.390405231	14.81499996
+1518	0.390463274	14.944426519
+1522	0.392151819	14.915203734
+1524	0.393186661	14.961747551
+1526	0.394158427	15.037075056
+1573	0.408168072	16.133197125
+1598	0.416766067	16.678992988
+1660	0.44328243	18.142114009
+1665	0.444965405	18.25355816
+1666	0.444720035	18.28403416
+1667	0.446062015	18.284690403
+1668	0.446125714	18.329058714
+1670	0.446133206	18.572377324
+1672	0.446952057	18.695455536
+1708	0.456918651	18.790907562
+1712	0.458244796	18.905278887
+1720	0.461813708	19.17002062
+1728	0.465456384	19.392921399
+1736	0.46909665	19.581211756
+1738	0.469009293	19.63986836
+1739	0.470088086	19.654523832
+1745	0.472925164	19.834706477
+1747	0.476427047	19.882721961
+1756	0.477945503	20.126510562
+1776	0.48555338	21.050697212
+1779	0.487291725	20.769860328
+1785	0.487422511	20.95968171
+1792	0.490868025	21.171034734
+1799	0.495984897	21.381192056
+1829	0.500577054	22.305283908
+1835	0.501130431	22.349754728
+1841	0.499636037	22.458577516
+1853	0.502867922	22.789015879
+1857	0.503177778	22.824136936
+1863	0.506992088	22.968349427
+1869	0.511573083	23.149349308
+1870	0.510409209	23.185619132
+1891	0.51604806	23.597859463
+1915	0.52134704	23.854239145
+1927	0.526302999	24.077963239
+1935	0.529154809	24.256248614
+1951	0.533841463	24.888246072
+1972	0.537198755	25.293137881
+1978	0.538614268	25.390662904
+2032	0.565800375	26.03466246
+2053	0.559773001	26.420268108
+2101	0.569853806	27.579091597
+2125	0.575521253	28.225772617
+2137	0.57871672	28.277690829
+2155	0.581133036	28.500376699
+2158	0.582197362	28.494612045
+2167	0.584903052	28.531839432
+2170	0.588296814	28.575386555
+2172	0.588168789	28.727190877
+2202	0.601001684	29.645737322
+2214	0.607209659	30.433077486
+2218	0.610239584	30.515088605
+2224	0.612489408	30.80970033
+2228	0.609919931	30.970134524
+2246	0.616805458	30.836588838
+2364	0.688856681	36.422097475
+2382	0.699198195	37.22853454
+2386	0.699697687	37.399438633
+2390	0.696379643	37.491589119
+2448	0.722756074	40.559368969
+2822	0.892213459	56.246352395
+2894	0.925655807	58.298946257
+2902	0.930451456	58.91838622
+2908	0.934032602	59.191770267
+2915	0.939078333	59.149010129
+3042	0.979294733	63.624004421
+3109	1.008006854	66.701448478
+3164	1.030117558	69.210002572
+3172	1.028983357	68.766214254
+3326	1.06337783	72.518414203
+3364	1.080085845	75.032993864
+3368	1.081815962	74.785882543
+3380	1.086156479	75.969527635
+3406	1.095992942	76.987838799
+3410	1.11796171	79.799157453

content/hopcroft_a.table

@@ -0,0 +1,15 @@
+states	Hopcroft	Moore
+4	0.000004394	0.000008367
+8	0.000007727	0.000020106
+16	0.000014457	0.000052275
+32	0.000030602	0.000155723
+64	0.000072037	0.000509607
+128	0.000193457	0.001816708
+256	0.000563881	0.00676876
+512	0.00145047	0.026100461
+1024	0.003533843	0.101946121
+2048	0.008529486	0.407693
+4096	0.021424756	1.64542877
+8192	0.051799602	6.570335332
+16384	0.12096594	26.285563125
+32768	0.295170838	106.794193669

content/hopcroft_b.table

@@ -0,0 +1,15 @@
+states	Hopcroft	Moore
+4	0.000004181	0.00000485
+8	0.000007397	0.000012002
+16	0.000013752	0.000030596
+32	0.000027895	0.000084655
+64	0.000061301	0.000258466
+128	0.000149001	0.00085492
+256	0.000390771	0.003013328
+512	0.000959998	0.011248316
+1024	0.002402636	0.043437952
+2048	0.005954948	0.1706022
+4096	0.015253576	0.684592527
+8192	0.035884835	2.758716619
+16384	0.082455912	11.050600273
+32768	0.194492715	43.719043747

content/minimal-separating-sequences.tex

@@ -647,9 +647,60 @@ This can be done in $\bigO(n^2)$ time using a trie data structure.
 
 
 \stopsection
+\startsection
+  [title={Experimental Results}]
 
-\todo{ga verder bij \tt 732}
+We have implemented \in{Algorithms}[alg:increase-k, alg:increase-k-v3] in Go, and we have compared their running time on two sets of FSMs.
+\footnote{Available at \todo{https://gitlab.science.ru.nl/rick/partition/}.}
+The first set is from \cite{Smeenk}, where FSMs for embedded control software were automatically constructed.
+These FSMs are of increasing size, varying from 546 to 3~410 states, with 78 inputs and up to 151 outputs.
+The second set is inferred from \citet[Hopcroft1971], where two classes of finite automata, $A$ and $B$, are described that serve as a worst case for \in{Algorithms}[alg:increase-k, alg:increase-k-v3] respectively.
+The FSMs that we have constructed for these automata have 1 input, 2 outputs, and $2^2$~--~$2^{15}$ states.
+The running times in seconds on an Intel Core i5-2500 are plotted in \in{Figure}[fig:results].
+We note that different slopes imply different complexity classes, since both axes have a logarithmic scale.
 
+\startplacefigure
+  [title={Running time in seconds of \in{Algorithm}[alg:increase-k] (grey) and \in{Algorithm}[alg:increase-k-v3] (black).},
+   reference=fig:results]
+\startcombination[2*1]
+{\starttikzpicture
+\startloglogaxis[width=0.5\textwidth, xtick={500, 1000, 2000, 3000}, xticklabels={500, 1000, 2000, 3000}]
+\addplot[color=darkgray] table[x=states, y=Moore]    {esm.table};
+\addplot[color=black]    table[x=states, y=Hopcroft] {esm.table};
+\stoploglogaxis
+\stoptikzpicture} {(a) Embedded control software.}
+{\starttikzpicture
+\startloglogaxis[width=0.5\textwidth, xtick={4, 64, 2048, 32768}, xticklabels={$2^2$, $2^6$, $2^{11}$, $2^{15}$}]
+\addplot[color=darkgray, dashed] table[x=states, y=Moore]    {hopcroft_b.table};
+\addplot[color=black, dashed]    table[x=states, y=Hopcroft] {hopcroft_b.table};
+\addplot[color=darkgray] table[x=states, y=Moore]    {hopcroft_a.table};
+\addplot[color=black]    table[x=states, y=Hopcroft] {hopcroft_a.table};
+\stoploglogaxis
+\stoptikzpicture} {(b) Class $A$ (dashed) and class $B$ (solid).}
+\stopcombination
+\stopplacefigure
+
+
+\stopsection
+\startsection
+  [title={Conclusion}]
+
+In this paper we have described an efficient algorithm for constructing a set of minimal-length sequences that pairwise distinguish all states of a finite state machine.
+By extending Hopcroft's minimisation algorithm, we are able to construct such sequences in $\bigO(m \log n)$ for a machine with $m$ transitions and $n$ states.
+This improves on the traditional $\bigO(mn)$ method that is based on the classic algorithm by Moore.
+As an upshot, the sequences obtained form a characterisation set and a separating family, which play a crucial in conformance testing.
+
+Two key observations were required for a correct adaptation of Hopcroft's algorithm.
+First, it is required to perform splits in order of the length of their associated sequences.
+This guarantees minimality of the obtained separating sequences.
+Second, it is required to consider nodes as a candidate before any one of its children are considered as a candidate.
+This order follows naturally from the construction of a splitting tree.
+
+Experimental results show that our algorithm outperforms the classic approach for both worst-case finite state machines and models of embedded control software.
+Applications of minimal separating sequences such as the ones described by \citet[dorofeeva2010fsm, Smeenk] therefore show that our algorithm is useful in practice.
+
+
+\stopsection
 \referencesifcomponent
 \stopchapter
 \stopcomponent

environment/tikz.tex

@@ -3,6 +3,8 @@
 \usemodule[tikz]
 \usetikzlibrary[automata, arrows, positioning, matrix, fit, decorations.pathreplacing]
 
+\usemodule[pgfplots]
+
 % defaults
 \tikzset{node distance=2cm} % 'shorten >=2pt' only for automata