This thesis proposes a novel, general and elegant proof search method, named Relevance-Zone-Oriented Proof (RZOP) search that uses relevance zones to help solve many positions in Connect6 as well as Connect games. In theory, this method can be applied to Connect games with infinite boards. Practically, this thesis demonstrates the method by solving two typical winning positions in Figure 7 (a) and Figure 7 (b) on 19 × 19 boards, as well as many Connect6 positions and openings in Appendix A. In addition, the method can also be easily incorporated into Connect6 program, such as NCTU6.
This thesis also leaves some open problems.
Investigate more winning positions in Connect6 that require Λ4-strategies, such as the one in Figure 7 (b).
Investigate whether there exists a Λ5-strategy in Connect6.
Apply the new method (in the Appendix D) to solving some real positions in general Connect games.
Investigate whether dual lambda search [48][49] is useful for Connect6 or Connect games.
Using the JL-PN search together with our RZOP search, we successfully solved up to 65 positions with Λ3-strategy. The 65 positions include 12 openings; in particular, Mickey-Mouse Opening, which used to be one of the popular openings before we solved it.
One might ask whether or when Connect6 on 19 × 19 boards will be solved. So far, we still
well balanced for both players. Hence, the answer to this question is still unknown.
In addition, this thesis further improves the RZOP method, named Segmented Relevance-Zone-Oriented Proof (SRZOP) search that speeds up the time to solve Connect6 positions. The experimental results in Chapter 5 archive 2.04 speedups to solve the 12 openings. This thesis also demonstrates records of our Connect6 program NCTU6 in Appendix F, which won the gold in the 11th and 13th Computer Olympiads in 2006 and 2008, respectively; and also won eight games and lost none against top Connect6 players in Taiwan in 2009. Finally, this thesis applies the RZOP method and SRZOP method into NCTU6 and NCTU6-verifiers which are used in the two systems (described in Subsection 5.1.3 and 5.1.4): (a) desktop grid system (b) JL-PN system. These two systems help us solve many Connect6 openings automatically. The author is very proud to announce this thesis because it is a milestone of NCTU6 and NCTU6-verifiers since year 2005 [65][66].
References
[1] L.V. Allis, Searching for solutions in games and artificial intelligence, Ph.D. Thesis, University of Limburg, Maastricht, The Netherlands, 1994.
[2] L.V. Allis, H.J. van den Herik and M.P.H. Huntjens, “Go-Moku Solved by New Search Techniques,” Computational Intelligence, vol. 12, pp. 7–23, 1996.
[3] L.V. Allis, M. van der Meulen and H.J. van den Herik, “Proof-number Search,” Artificial Intelligence, vol. 66 (1), pp. 91–124, 1994.
[4] D.P. Anderson, “Boinc: A System for Public-resource Computing and Storage,”
Proceedings of the Fifth IEEE/ACM International Workshop on Grid Computing (GRID'04), IEEE CS Press, Pittsburgh, USA, pp. 4-10, 2004.
[5] J. Beck, “On Positional Games,” Combinatorial Theory Series A 30, pp. 117–133, 1981.
[6] C. Berge, Graphs and Hypergraphs, North Holland, Amsterdam, 1973.
[7] E.R. Berlekamp, J.H. Conway and R.K. Guy, Winning Ways for your Mathematical Plays, vol. 3, 2nd ed., A K Peters. Ltd. Canada, 2003.
[8] BOINC, Available: http://boinc.berkeley.edu/.
[9] D.M. Breuker, J. Uiterwijk and H. J. van den Herik, “The PN2-search Algorithm,” in H. J.
van den Herik, B. Monien (Eds.), Advances in Computer Games, vol. 9, IKAT, Universiteit Maastricht, Maastricht, The Netherlands, pp. 115–132, 2001.
[10] A. de Bruin, W. Pijls and A. Plaat, “Solution Trees as a Basis for Game-Tree Search,”
ICCA Journal, vol 17(4), pp. 207–219, December 1994.
[11] T. Cazenave, “Abstract Proof Search,” Computers and Games (eds. T. A. Marsland and I.
Frank), Lecture Notes in Computer Science, vol. 2063, pp. 39–54, 2001.
[12] T. Cazenave, “A Generalized Threats Search Algorithm,” Computers and Games, Lecture Notes in Computer Science, vol. 2883, pp. 75–87, 2003.
[13] G.M. Chaslot, M.H.M. Winands and H.J. van den Herik, “Parallel Monte-Carlo Tree
[14] C.-P. Chen, I.-C. Wu and Y.-C. Chan, “ConnectLib – A Connect6 Editor,” Available:
http://www.connect6.org/Connect6Lib_Manual.htm, 2009.
[15] S.-H. Chiang, I.-C. Wu and P.-H. Lin, “On Draw K-in-a-row Games,” Advances in Computer Games Conference (ACG2009), vol. 6048, pp. 158–169, 2010.
[16] Chinese Association for Artificial Intelligence, Chinese Computer Games Contest (in Chinese), Available: http://www.caai.cn/.
[17] L. Csirmaz, “On a Combinatorial Game with An Application to Go-moku,” Discrete Math.
29, pp. 19–23, 1980.
[18] R. Diestel, Graph Theory, Springer, New York, 2nd edition, 2000.
[19] G. Fedak, C. Germain, V. Neri and F. Cappello, “Xtremweb: A Generic Global Computing System,” Proceedings of the 1st IEEE/ACM International Symposium on Cluster Computing and the Grid (CCGRID2001): Workshop on Global Computing on Personal Devices, IEEE CS Press, Brisbane, Australia, pp. 582–587, 2001.
[20] I. Foster, C. Kesselman, The Grid: Blueprint for a New Computing Infrastructure, Morgan Kaufmann Publishers, Inc., 1999.
[21] The globus project, Available: http://www.globus.org/.
[22] H.J. van den Herik, J.W.H.M. Uiterwijk and J.V. Rijswijck, “Games solved: Now and in the future,” Artificial Intelligence, vol. 134 (1-2), pp. 277–311, 2002.
[23] H.J. van den Herik and M.H.M. Winands, “Proof-Number Search and its Variants,”
Oppositional Concepts in Computational Intelligence, pp. 91-118, 2008.
[24] M.-Y. Hsieh and S.-C. Tsai, “On the Fairness and Complexity of Generalized K-in-a-row Games,” Theoretical Computer Science, vol. 385, pp. 88–100, 2007.
[25] Yu-Chun Huang, private communication, 2008.
[26] B. Jacob, L. Ferreira, N. Bieberstein, C. Gilzean, J.Y. Girard, R. Strachowski and S.S. Yu, Enabling Applications for Gird Computing with Globus, IBM Redbooks, 2003.
[27] A. Kishimoto and Y. Kotani, “Parallel AND/OR Tree Search Based on Proof and Disproof Numbers,” Fifth Games Programming Workshop, vol. 99(14) of IPSJ Symposium Series, pp. 24–30, 1999.
[28] A. Kishimoto and M. Müller, “A general solution to the graph history interaction problem,” Nineteenth National Conference on Artificial Intelligence (AAAI2004), pp.
644–649, San Jose, CA, 2004.
[29] A. Kishimoto and M. Müller, “Search versus Knowledge for Solving Life and Death Problems in Go,” Twentieth National Conference on Artificial Intelligence (AAAI2005), pp. 1374–1379, 2005.
[30] P.-H. Lin and I.-C. Wu, “NCTU6 Wins Man-Machine Connect6 Championship 2009,”
ICGA Journal, vol. 32(4), pp. 230–232, 2009.
[31] P.-H. Lin and I.-C. Wu, “Segmented Relevance-Zone-Oriented Proof Search for Connect6,” in preparation, 2010.
[32] T.W. Lee, One of Early Tsumegos for Connect6, Available:
http://www.connect6.org/web/index.php?option=com_tsumego&task=loadTsumegoHistor yList&class_id=32, 2005.
[33] Littlegolem, Online Connect6 games, Available: http://www.littlegolem.net/, 2006.
[34] V. Manohararajah, Parallel Alpha-beta Search on Shared Memory Multiprocessors, Master’s thesis, Graduate Department of Electrical and Computer Engineering, University of Toronto, Canada, 2001.
[35] A. Nagai, Df-pn Algorithm for Searching AND/OR Trees and Its Applications, Ph.D.
thesis, University of Tokyo, Japan, 2002.
[36] J. Pawlewicz and L. Lew, “Improving Depth-first pn-search: 1+ε Trick,” In H. J. van den Herik, P. Ciancarini, and H.H.L.M. Donkers, editors, Fifth International Conference on Computers and Games, vol. 4630 of LNCS, pp. 160–170, Computers and Games, Springer, Heidelberg, 2006.
[37] W. Pijls and A. de Bruin, “Game Tree Algorithms and Solution Trees,” Computers and Games, Lecture Notes in Computer Science, vol. 1558, pp. 195–204, 1999.
[38] A. Pluhar, “The Accelerated K-in-a-row Game,” Theoretical Computer Science, vol.
270(1-2), pp. 865–875, 2002.
[39] V. N. Rao and V. Kumar, “Superlinear Speedup in State-space Search,” Proceedings of the 1988 Foundation of Software Technology and Theoretical Computer Science, no. 338 of LNCS, pp. 161–174, Springer-Verlag, 1988.
[40] Red-bean.com, SGF File Format, Available: http://www.red-bean.com/sgf/.
http://www.renju.net/study/rifrules.php, 1998.
[42] Renlib, Renju – A Ranju Editor, Available: http://www.renju.se/renlib/.
[43] J.T. Saito, M.H.M. Winands and H.J. van den Herik, “Randomized Parallel Proof-Number Search,” Advances in Computer Games Conference (ACG2009), Lecture Notes in Computer Science (LNCS 6048), pp. 75–87, Palacio del Condestable, Pamplona, Spain, 2009.
[44] G. Sakata and W. Ikawa, Five-In-A-Row, Renju. The Ishi Press, Inc., Tokyo, Japan, 1981.
[45] J. Schaeffer, N. Burch, Y.N. Björnsson, A. Kishimoto, M. Müller, R. Lake, P. Lu and S.
Sutphen, “Checkers is Solved,” Science, vol. 5844(317), pp. 1518–1552, 2007.
[46] M. Seo, H. Iida and J. Uiterwijk, “The PN*-search algorithm: Application to Tsumeshogi,” Artificial Intelligence, vol. 129(1-2), pp. 253–277, 2001.
[47] SETI@home, Available: http://setiathome.ssl.berkeley.edu.
[48] S. Soeda, T. Kaneko and T. Tanaka, “Dual Lambda Search and its Application to Shogi Endgames,” Advances in Computer Games Conference (ACG2005), Taipei, Taiwan, 2005.
[49] S. Soeda, T. Kaneko and T. Tanaka, “Dual Lambda Search and Shogi Endgames,”
Advances in Computer Games Conference (ACG'11), Lecture Notes in Computer Science, vol. 4250, pp. 126–139, 2006.
[50] Taiwan Connect6 Association, Connect6 homepage, Available: http://www.connect6.org/.
[51] ThinkNewIdea Inc, CYC game (in Chinese), Available: http://cycgame.com/, 2005.
[52] T. Thomsen, “Lambda-Search in Game Trees - With Application to Go,” ICGA Journal, vol. 23(4), pp. 203–217, 2000.
[53] J. Wagner and I. Virag, “Solving Renju,” ICGA Journal, vol. 24(1), pp. 30–34, 2001.
[54] M.H.M. Winands, J.W.H.M. Uiterwijk and H.J. van den Herik, “PDS-PN: A new proof-number search algorithm: Application to Lines of Action,” In J. Schaeffer, M.
Müller, and Y. Björnson, editors, Computers and Games 2002, vol. 2883 of LNCS, pp.
170–185. Computers and Games, Springer, Heidelberg, 2003.
[55] I.-C. Wu, Proposal for a New Computer Olympiad Game – Connect6, Available:
http://ticc.uvt.nl/icga/news/Olympiad/Olympiad2006/connect6.pdf, or http://www.connect6.org/articles/RZOP/connect6.pdf, 2005.
[56] I.-C. Wu, B.-H. Lin, L.-B. Chen, J.-Y. Su and P.-C. Hsu, “HybridDiff: An Algorithm for A New Tree Editing Distance Problem,” International Computer Symposium (ICS2006), Taipei, Taiwan, 2006.
[57] I.-C. Wu, C.-P. Chen, P.-H. Lin, K.-C. Huang, L.-P. Chen, D.-J. Sun, Y.-C. Chan and H.-Y.
Tsou, “A Volunteer-Computing-Based Grid Environment for Connect6 Applications,”
IEEE International Conference on Computational Science and Engineering (CSE2009), vol. 1, pp. 110–117, 2009.
[58] I.-C. Wu, C.-P. Chen, P.-H. Lin, G.-Z. Huang, L.-P. Chen, D.-J. Sun and H.-Y. Tsou, “A Desktop Grid Computing Service for Connect6 Applications,” International Symposium on Grid Computing (ISGC2009), Taipei, Taiwan, 2009.
[59] I.-C. Wu and P.-H. Lin, “NCTU6-Lite Wins Connect6 Tournament,” ICGA Journal, vol.
31(4), pp. 240–243, 2008.
[60] I.-C. Wu and P.-H. Lin, “Relevance-Zone-Oriented Proof Search for Connect6,” IEEE Transaction on Computational Intelligence and AI in Games, vol. 2(3), September 2010.
[61] I.-C. Wu and P.-H. Lin, Benchmark for RZOP search, Available:
http://www.connect6.org/articles/RZOP/.
[62] I.-C. Wu and P.-H. Lin, Benchmark for SRZOP search, Available:
http://www.connect6.org/articles/SRZOP/.
[63] I-C. Wu and P.-H. Lin, Search tree for drawn Connect(11,2), Available:
http://www.connect6.org/articles/drawn-connect-games/.
[64] I.-C. Wu, H.-H. Lin, P.-H. Lin, D.-J. Sun, Y.-C. Chan and B.-T. Chen, “Job-Level Proof-Number Search for Connect6,” International Conference on Computers and Games (CG2010), Kanazawa, Japan, 2010.
[65] I.-C. Wu, D.-Y. Huang and H.-C. Chang, “Connect6,” ICGA Journal, vol. 28(4), pp.
234–242, 2006.
[66] I.-C. Wu and D.-Y. Huang, “A New Family of K-in-a-row Games,” Advances in Computer Games Conference (ACG2005), Taipei, Taiwan, 2005.
[67] I.-C. Wu and S.-J. Yen, “NCTU6 Wins Connect6 Tournament,” ICGA Journal, vol. 29(3), pp. 157–158, September 2006.
[69] T. G. L. Zetters, “8(or more) In a Row,” American Mathematical Monthly 87, pp. 575–576, 1980.
Appendix A Sample Positions
Figure 34. 65 winning positions.
01 02
05 06
07 08
09 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
Appendix B Results of RZOP Benchmark
Table 9. The solvability of verifiers for 65 winning positions in Appendix A, where “yes”
means solved and “no” means unsolved.
18 yes yes
42 yes no
Total solved 65 31
Total unsolved 0 34
Appendix C Results of SRZOP Benchmark
Table 10. The statistics of verifiers for 65 winning positions in Appendix A: (a) number of nodes and (b) times.
18 67852 69610 71727
42 4045655 4046601 5511607
Total 178020119 179532383 304485291
22 16.27 16.25 16.34
46 84.09 85.14 86.02
Appendix D Verifiers for General Connect Games
In this Appendix, the verifier VC6(P,S) is generalized to general Connect games, Connect(m,n,k,p,q), while maintaining Property RZV.
The generalized verifier is denoted by VCK(P,S). In the case that P is an endgame position or is in Attacker’s turn (described in Subsections 3.2.1 and 3.2.2 respectively), the verifier VCK(P,S) is the same as VC6(P,S). So, the rest of this appendix describes the verifier only in the case that P is in Defender’s turn. Furthermore, the position P (in Defender’s turn) can be classified into the following two. (1) The number of Attacker threats t in P is at least p + 1, and (2) the number t is at most p. In the first case, Attacker wins already. Therefore, the verifier returns 1 and construct relevance zones in the following operation.
Tp1-1. Construct relevance zones by following both operations T3-1 and T3-2, except that the terms “i + 2” are replaced by “i + p”.
Similar to Lemma 7, Lemma 31 shows that the verifier also satisfies Property RZV in this case.
Lemma 31. Assume that Defender is to move and the number of Attacker threats is at least p + 1 in P. The verifier described above satisfies Property RZV.
Proof. The proof is similar to that of Lemma 7 and therefore omitted. ▌
In the second case that the number of Attacker threats t is at most p, the verifier performs the following operations.
Tp-1. For each of critical defenses MD (both normal and relaxed), perform the following.
a. Return 0 if the sub-verifier Vsub(MD,P,S) returns 0. Note that the sub-verifier is described below.
b. Let Ψ(P) = Ψ(P) ∪ Ψ'(PD).
Tp-2. Continue to construct relevance zones in operation Tp1-1, and return 1.
In operation Tp-1.a, a sub-verifier Vsub(MD,P,S) is used to verify whether Attacker wins for all Defender moves M'D dominated by MD in P, where M'D has p squares (but MD may have less than p squares). By dominate, we mean that all squares in MD must also be in M'D, but may not vice versa. For the sub-verifier Vsub(MD,P,S), the constructed zones is denoted by Ψ'(PD) = <Z'1(PD), Z'2(PD), …, Z'r(PD)>, where PD = P⊕MD. In addition, the sub-verifier satisfies the following property (proved in Lemma 32).
Property RZS. If Vsub(MD,P,S) returns 1, the following condition holds. For all Defender moves M'D dominated by MD, there exists some Ψ'D such that Ψ'D⊆ Ψ'(PD) and Ψ'D is in RZ(P⊕M'D).
The sub-verifier Vsub(MD,P,S) performs the following operations.
Par-1. Assume that MD has exactly p – u Defender stones, where u is the number of null stones in MD and 0 ≤ u ≤ p. In the case that u > 0, move MD is a null or semi-null move.
Par-2. Return 0 if VCK(PD,S) returns 0, where PD = P⊕MD.
Par-5. For each of unoccupied square s∈¬PD(Zu(PD)), perform the following.
a. Let Defender move MD,s be MD + σD(s).
b. Return 0 if Vsub(MD,s,P,S) returns 0.
c. Let Ψ'(PD) = Ψ'(PD) ∪ Ψ'(PD,s), where PD,s = P⊕MD,s. Par-6. Return 1.
Lemma 32 shows that the sub-verifier satisfies Property RZS, if all the recursive Vsub in Par-5.b satisfy Property RZS and the verifier VCK in Par-2 satisfies Property RZV.
Lemma 32. For a sub-verifier Vsub(MD,P,S) as described above, it satisfies Property RZS by assuming that all the recursive Vsub in Par-5.b satisfy Property RZS and that the verifier VCK
in Par-2 satisfies Property RZV.
Proof. Assume that Vsub(MD,P,S) returns 1. Consider all Defender moves M'D (including p stones) that are dominated by MD. Namely, let M'D = MD + σD(ϕ), where ϕ has u additional unoccupied squares. For this lemma, it suffices to prove that there exists some Ψ'D such that Ψ'D⊆ Ψ'(PD) and Ψ'D is in RZ(P⊕M'D). All of these Defender moves M'D are classified into the following cases.
1. All Defender moves M'D in which all additional squares s in ϕ are in ¬PD(Zu(PD)).
The proof for this case is similar to that for Case 1 in Lemma 10 as follows. Since this sub-verifier returns 1, the verifier VCK(PD,S) in Par-2 returns 1. Since the verifier VCK returns 1 and also satisfies Property RZV (from this lemma), Ψ(PD) is in RZ(PD).
sub-verifier returns 1, the recursive Vsub(MD,s,P,S) at Par-5.b returns 1 too and therefore satisfies Property RZS. From Property RZS, there exists some Ψ such that Ψ ⊆ Ψ'(PD,s) and Ψ is in RZ(P⊕M'D). Since Ψ'(PD,s) ⊆ Ψ'(PD) from operation Par-5.c, we obtain Ψ ⊆ Ψ'(PD). Thus, Ψ is the Ψ'D. ▌
From Lemma 32, we derive Lemma 33 as follows.
Lemma 33. Assume that Defender is to move and the number of Attacker threats is at most p in P. The verifier described above satisfies Property RZV by assuming that all the recursive sub-verifiers in operation Tp-1.a satisfy Property RZS.
Proof. Assume that this verifier returns 1. For this lemma, it suffices to prove that the constructed Ψ(P) is in RZ(P). Since the verifier returns 1, all the recursive sub-verifiers in operation Tp-1.a returns 1 too. Assume that these sub-verifiers satisfy Property RZS. For proving Ψ(P)∈RZ(P), it suffices to prove from Lemma 6 the following: For all Defender moves MD there exists some ΨD such that ΨD is in RZ(P⊕MD) and ΨD ⊆ Ψ(P). All Defender moves MD are classified into the following two cases:
1. All Defender moves MD that block all the threats. There must exist some critical defense M'D (either normal or relaxed) dominating MD. Since Vsub(M'D,P,S) returns 1 and satisfies Property RZS from above, there exists some ΨD from the property such that ΨD⊆ Ψ'(P⊕M'D) and ΨD is in RZ(P⊕M'D).
2. All Defender moves MD that leave some threat unblocked. Attacker wins by connecting up to p on some unblocked threat segment, like S3T. From the proof in Lemma 31, we obtain that there exists some ΨD such that ΨD⊆ Ψ'(P) and ΨD is in RZ(PD). ▌
Theorem 5 (below) concludes that the verifier VCK(P,S) in all cases satisfy Property RZV. Therefore, if VCK(P,S) returns 1, the constructed Ψ(P) is in RZ(P), and Attacker wins in P from Corollary 2. It can also be observed that the operations in Subsection 3.2.3 are special cases of the operations described in this appendix.
Theorem 5. The verifier VCK(P,S) satisfies Property RZV in all cases.
Proof. By induction, the verifier VCK(P,S) satisfies Property RZV in all cases from the above lemmas. ▌
Appendix E Draw K-in-a-row Games
In the past, many researchers were engaged in solving Connect(m, n, k, p, q) games.
One player, either Black or White, is said to win a game, if he has a winning strategy such that he wins for all the subsequent moves. Allis et al. [1][2] solved Go-Moku with Black winning. Herik et al. [22] and Wu et al. [65][66] also mentioned several k-in-a-row games with Black winning.
A game is said to be drawn if neither player has any winning strategy. For simplicity, Connect(k, p) refers to the collection of Connect(m, n, k, p, q) games for all m ≥ 1, n ≥ 1, 0 ≤ q ≤ p. Connect(k, p) is said to be drawn if all Connect(m, n, k, p, q) games in Connect(k, p) are drawn.
In the past, Zetters [69] derived that Connect(8, 1) is drawn. Pluhar [38] derived tight bounds kdraw(p) = p+Ω(log2p) for all p ≥ 1000 (cf. Theorem 1 in [38]). However, the requirement of p ≥ 1000 is unrealistic in real games. Thus, it is important to obtain tight bounds when p < 1000. Hsieh and Tsai [24] have recently derived that kdraw(p) = 4p+7 for all positive p. The ratio R = kdraw(p)/p is approximately 4 for sufficiently large p.
Given p, Chiang et al. [15] derive the value kdraw(p), such that Connect(m, n, k, p, q) are drawn for all k ≥ kdraw(p), m ≥ 1, n ≥ 1, 0 ≤ q ≤ p, as follows. (1) kdraw(p) = 11. (2) For all p ≥ 3, kdraw(p) = 3p+3d–1, where d is a logarithmic function of p. So, the ratio kdraw(p)/p is approximately 3 for sufficiently large p. The first result was derived with the help of a program. To our knowledge, our kdraw(p) values are currently the smallest for all 2 ≤ p <
1000.
Appendix F Author’s Records
The game Connect6 was first introduced by Wu and Huang (2005) and then described in more detail by Wu, Huang and Chang (2006). The rules of Connect6 are very simple.
Two players, henceforth represented as B (designated as the first player) and W, alternately place two stones, black and white respectively, on one empty intersection of an 19×19 board, except for that B places one stone initially. The player who first obtains six consecutive stones (horizontally, vertically or diagonally) wins the game. When all intersections on the board are occupied without connecting six, the game draws.
Starting from 2007, Lin became the chief designer of the Connect6 program NCTU6.
Though, NCTU6 won the Gold Prize of the Connect6 Tournament in the 11th Computer Olympiad (2006), there were many unsolved positions and openings. Thus, Lin solved many unsolved VCST positions in the beginning and help developed some simple openings.
With the improved strength of NCTU6, Lin developed a light weight version with accurate time control program named NCTU6-LITE, which won the Gold Prize of the Connect6 Tournament in the 13th Computer Olympiad (2008). The participants and the final standings are listed in Table 11 (below).
In the tournament, the games were played according to a round-robin system in which one program played twice against all the other programs. In each game, every program had to complete all of its moves in 30 minutes. For each game, the winner scored 1 point and the loser scored nothing. However, for a draw game, both scored 0.5. Figure 35 and Figure 36 (below) show some events in the 13th Computer Olympiad. The certificate of the 13th Computer Olympiad by NCTU is shown in Figure 37 (below).
Ranking Program Author Organization Points
3 NEUCONN6 Chang-Ming Xu Northeastern
University, China 13
8 CV6
Table 11. The participants and the final standings of the Connect6 Tournament in the 13th Computer Olympiad (2008).
Figure 35. P. H. Lin, I-C. Wu and H.J. van den Herik.
Figure 36. L. Lee (BITSTRONGER) and P. H. Lin (NCTU6-LITE).
In Taiwan, National Chiao Tung University hosts the annual NCTU Cup Open Tournaments for Connect6 human players. We saw more and more players played Connect6 every year. Before the second annual NCTU Cup Open Tournament 2008 took place, Wu invited Go Champion Chou Jun Xun to play Connect6 against the AI program NCTU6 for the advertisement. In this championship, NCTU6 won 3 and lost nothing against Chou.
Figure 38 shows an event in the championship.
Figure 38. Go Champion Chou Jun Xun, the operating staff and P. H. Lin.
After annual NCTU Cup Open Tournaments, yearly top human players of Connect6 will appear. To survey the strength of NCTU6, Wu will invite three to four top players to play against NCTU6. Figure 39 and Figure 40 (below) show events of the first and the second Man-Machine Connect6 Championships.
Figure 39. Professor Shun-Chin Hsu (right most) and members of the Connect6 team lead by I-C. Wu.
In Figure 39, Professor Shun-Chin Hsu is respected as the father of Computer Chinese Chess. He has received many awards and published many important papers. In the first annual Man-Machine Connect6 Contest, we are very happy to invite Professor Hus to host the contest. In the contest, NCTU6 won 11 and lost one against top human players. It is a good record. Next year, in the second annual Man-Machine Connect6 Contest, NCTU6 won 8 and lost nothing which is a memorable record.
From these records, Lin proved the strength of NCTU6. He will continue to develop NCTU6 and keep NCTU6 the top AI program of Connect6 in the world.
Vita
Ping-Hung Lin was born in Hualien, Taiwan in 1978. He received the B.S.,
Ping-Hung Lin was born in Hualien, Taiwan in 1978. He received the B.S.,