What is "mex"

MEX (Multiple EXposure) was " Silicon Graphics' original high-performance windowing system", used on 68k-based IRIS systems and early IRIS 4D systems. MEX was originally loaded over a network through the utilization of GL1 routines kept on a remote host machine, usually a VAX. When the IRIS 1400 workstation and GL2-W ( IRIX) were introduced, MEX was allowed to run locally. MEX was used in IRIX from the GL2-W2.1.0 release to the 4D1-2.3 release.

With the introduction of 4D1-3.0 (IRIX 3.0), and the complete migration to MIPS processors, support for the GL / GL2 powered MEX ended in the late 1980s, replaced by Sun Microsystems' NeWS and the 4Sight window manager.

In combinatorial game theory, the mex, or "minimum excludant", of a set of ordinals denotes the smallest ordinal not contained in the set.

Some examples:

mex(∅) = 0

mex({1, 2, 3}) = 0

mex({0, 2, 4, 6, …}) = 1

mex({0, 1, 4, 7, 12}) = 2

mex({0, 1, 2, 3, …}) = ω

mex({0, 1, 2, 3, …, ω}) = ω + 1

where is the limit ordinal for the natural numbers.

In the Sprague-Grundy theory the minimum excluded ordinal is used to determine the nimber of a normal-play impartial game, which is a game in which either player has the same moves in each position and the last player to move wins. The nimber is equal to 0 for a game that is lost immediately by the first player, and is equal to the mex of the nimbers of all possible next positions for any other game.

For example, in a one-pile version of Nim, the game starts with a pile of stones, and the player to move may take any positive number of stones. If is zero stones, the nimber is 0 because the mex of the empty set of legal moves is the nimber 0. If is 1 stone, the player to move will leave 0 stones, and , gives the nimber for this case. If is 2 stones, the player to move can leave 0 or 1 stones, giving the nimber 2 as the mex of the nimbers { 0, 1 }. In general, the player to move with a pile of stones can leave anywhere from 0 to stones; the mex of the nimbers is always the nimber . The first player wins in Nim if and only if the nimber is not zero, so from this analysis we can conclude that the first player wins if and only if the starting number of stones in a one-pile game of Nim is not zero; the winning move is to take all the stones.

If we change the game so that the player to move can take up to 3 stones only, then with stones, the successor states have nimbers , giving a mex of 0. Since the nimber for 4 stones is 0, the first player loses. The second player's strategy is to respond to whatever move the first player makes by taking the rest of the stones. For stones, the nimbers of the successor states of 2, 3, and 4 stones are the nimbers 2, 3, and 0 (as we just calculated); the mex of the set of nimbers is the nimber 1, so starting with 5 stones in this game is a win for the first player.

See nimbers for more details on the meaning of nimber values.

MEX may refer to:

• MEX (windowing system), Silicon Graphics' original high-performance windowing system
• MEX file, a type of C/C++ or FORTRAN source code in MATLAB scripts
• Mexico City International Airport, IATA airport code
• Mexico, IOC and FIFA country code
• Mars Express Orbiter, the European Space Agency mission to Mars
• Mexborough railway station, England; National Rail station code MEX
• Maju Expressway, an expressway in Kuala Lumpur, Malaysia

Mex may refer to:

• Several municipalities in Switzerland:
  • Mex, Vaud
  • Mex, Valais
• Mex (mathematics), a mathematical function in game theory

MeX may refer to:

• The MeX, a nickname for the Boyd Martin Theatre, one of the theatres of The Kentucky Center

1. redirect Mex, Vaud

1. redirect Mex, Valais