Mater

a chess mating combinations program, developed in the mid 60s by George Baylor and Herbert Simon, which was subject of Baylor's Masters thesis at Carnegie Mellon University. It was an early pioneering attempt in finding forced checkmates, employing "Artificial Intelligence" rather than "Brute-Force". Only moves which either put the enemy king in check (**Mater I**), or threaten mate in one (**Mater II**) were generated for the attacking side, searching those moves first which leave the minimum number of defensive replies, to eventually reduce the defender's mobility to zero. || toc =Abstract= This page is based on the description of Mater by George Baylor and Herbert Simon, 1966, //A chess mating combinations program// :
 * Home * Engines * Mater**
 * [[image:261px-Yale's_Hartmann_astrolabe.jpg link="http://commons.wikimedia.org/wiki/File:Yale%27s_Hartmann_astrolabe.jpg"]] ||~ || **Mater**,
 * [|Astrolabe], [|Mater] and [|Tympan] ||~ ||^ ||

=History= The original mating combination program, as conceived by Herbert Simon and his son Peter Simon in 1962, was a hand simulation setting forth a strategy of search. It discovered mating combinations in 52 of the 129 positions collected in [|Fine's] chapter of the mating attack from //The Middlegame in Chess//. Newell's and Prasad's [|IPL] program, which could set up a chessboard, recorded positions, generated and made moves and testing their legality, was base of **Mater I** and in 1964 the revised **Mater II** programs. According to Monroe Newborn, Mater was ported to Fortran and incorporated into Cooper-Kozdrowicki program by Dennis Cooper and Ed Kozdrowicki :

=Mater I= =Mater II=
 * [[image:http://webchess.freehostia.com/diag/chessdiag.php?fen=r1bk2nr/p2p1pNp/n2B4/1p1NP2P/6P1/3P1Q2/P1P1K3/q5b1%20w%20-%20-&size=medium&coord=no&cap=no&stm=no&fb=no&theme=classic&color1=E3CEAA&color2=635147&color3=000000]] ||~ || Only check giving moves were generated in **Mater I** for the attacking side and check evasions for the defending side, for each ply level put into a try-list. For the attacker, the list is ordered by the fewest-reply heuristic, highest priority goes to moves with the fewest number of legal replies, while checking moves with more than **four** legal replies are pruned entirely. Ties are broken by giving priority to double checks and then to checks with no capturing replies. Search only continues down a particular path so long as the opponent's mobility is on the decline, which implies a maximum search depth of 9 plies. The defender's side considers captures in MVV/LVA order first, followed by king moves and interpositions. In //A chess mating combinations program//, the beta-cutoff was mentioned as "killing reply", also with a footnote on McCarthy.'s killer heuristic referring Alan Kotok's 1962 paper , covering alpha-beta. [|Reuben Fine's] position from //The Middlegame in Chess// served as one example of Mater's ability . ||
 * [[image:http://webchess.freehostia.com/diag/chessdiag.php?fen=r1b2qrk/pp3p1p/4pPpQ/8/8/5N2/P4PPP/3R2KR%20w%20-%20-&size=medium&coord=no&cap=no&stm=no&fb=no&theme=classic&color1=E3CEAA&color2=635147&color3=000000]] ||~ || At its first level of search, **Mater II** also generates moves threatening mate in one. After generation and trying checking moves without success, but triggered after collecting useful informations of "nearly" mate with only one legal reply, Mater II considers none checking moves which put additional pressure to the enemy king's sector, that is moves which directly or indirectly (x-ray) attack squares around the king. In this respect it resembles what Adriaan de Groot has called a "sample variation", a kind of trial balloon sent up for the express purpose of gathering information to direct subsequent investigations. A further condition to finally add the move into the try-list is that after the move is internally made followed by a defender's null move, the resulting position is mate in one. Now, the defender's move ordering heuristic needs to prefer moves that defend the mating square. Fine's diagram 97 was given as example of the abilities of Mater II. ||

=Board Representation= Mater was written in [|IPL V] with its primary data structure of a list, and kept lists with a header (name) and [|attribute-value pairs] for each square and piece to represent the board, where values for piece and square attributes are addresses (cells) of lists again, yielding in an extensive network of relations among squares and pieces:


 * ~ Name ||~ Attribut ||~ Value ||
 * H1 || Man on square || M8 ||
 * || North || H2 ||
 * || West || G1 ||
 * || WNW  || F2 ||
 * || NW   || G2 ||
 * || NNW  || G3 ||
 * M8 || Man on what square || H1 ||
 * || Type of man || Rook ||
 * || Color of man || White ||
 * || Move directions || list of directions ||
 * || Capture directions || list of directions ||
 * || Capture directions || list of directions ||

=Move Generation= In //A chess mating combinations program//, Baylor and Simon further elaborate on move generation, with two tacks, corresponding to a **one-many** or **many-one** approach. In trying to find all checking moves, one could either radiate out from the enemy king, and for each square, search for a piece that can get there and check (one-many), or converge from the squares along the move directions of each attacking piece onto the enemy king's square (many-one). If there are many pieces on the board, the former tends to be more effective, if few, the latter.

=Processing Speed= Mater was written in an [|interpretive language] IPL, without any attempts to provide a special [|machine-language] representation for primitive board manipulation. The most difficult mates, requiring the examination of about 100 positions, were achieved in about 3 minutes on an IBM 7090.

=Namesake=
 * Mater by Valentin Albillo

=See also=
 * Astronomy
 * Chest
 * MAPP
 * Mate at a Glance
 * Mate-in-two
 * Mate Search
 * NSS
 * Perceiver

=Publications=
 * Herbert A. Simon, [|Peter A. Simon] (**1962**). //[|Trial and Error Search in Solving Difficult Problems: Evidence from the Game of Chess]//. Behavioral Science, Vol. 7, No. 4, pp. 425-429
 * George W. Baylor (**1965**). //[|Report on a Mating Combinations Program]//. SDC Paper, No. SP-2150, System Development Corporation, Santa Monica, Calif.
 * George W. Baylor, Herbert A. Simon (**1966**). //[|A chess mating combinations program]//. [|AFIPS] [|Joint Computer Conferences], reprinted  in Herbert A. Simon (**1979**). //[|Models of Thought]//. [|Yale University Press], pp. 181-200, in David Levy (ed.) (**1988**). //Computer Chess Compendium//.
 * George W. Baylor (**1966**). //A Computer Model of Checkmating Behaviour in Chess//. in Adriaan de Groot, Walter R. Reitman (eds.) (**1966**). //Heuristic Processes in Thinking//. International Congress of Psychology, [|Nauka], [|Moscow]
 * Herbert Simon (**1973**). //Lessons from Perception for Chess-Playing Programs (and Vice Versa)//. Computer Science Research Review 1972-73, [|pdf]
 * Herbert Simon, William Chase (**1973**). //Skill in Chess//. [|American Scientist], Vol. 61, No. 4, reprinted in David Levy (ed.) (**1988**) //Computer Chess Compendium//, [|pdf]
 * Max Bramer (**1982**). //Finding Checkmates//. [|Computer & Video Games], [|Spring 1982], [|pdf] hosted by Mike Watters

=External Links=
 * [|mater - Wiktionary]
 * [|Mater (disambiguation) from Wikipedia]
 * [|Alma mater from Wikipedia]
 * [|Alma mater (disambiguation) from Wikipedia]
 * [|Stabat Mater from Wikipedia]
 * [|Stata Mater from Wikipedia]

=References= =What links here?= include page="Mater" component="backlinks" limit="40"
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