% % Traffic lights problem in ASP. % % CSPLib problem 16 % http://www.csplib.org/Problems/prob016 % """ % Specification: % Consider a four way traffic junction with eight traffic lights. Four of % the traffic lights are for the vehicles and can be represented by the % variables V1 to V4 with domains % {r,ry,g,y} (for red, red-yellow, green and yellow). % The other four traffic lights are for the pedestrians and can be % represented by the variables P1 to P4 with domains {r,g}. % % The constraints on these variables can be modelled by quaternary % constraints on % (Vi, Pi, Vj, Pj ) for 1<=i<=4, j=(1+i)mod 4 which allow just the tuples % {(r,r,g,g), (ry,r,y,r), (g,g,r,r), (y,r,ry,r)}. % % It would be interesting to consider other types of junction (e.g. five roads % intersecting) as well as modelling the evolution over time of the % traffic light sequence. % ... % % Results % Only 2^2 out of the 2^12 possible assignments are solutions. % % (V1,P1,V2,P2,V3,P3,V4,P4) = % {(r,r,g,g,r,r,g,g), (ry,r,y,r,ry,r,y,r), (g,g,r,r,g,g,r,r), (y,r,ry,r,y,r,ry,r)} % [(1,1,3,3,1,1,3,3), ( 2,1,4,1, 2,1,4,1), (3,3,1,1,3,3,1,1), (4,1, 2,1,4,1, 2,1)} % % % The problem has relative few constraints, but each is very tight. % Local propagation appears to be rather ineffective on this problem. % % """ % % This was created by Hakan Kjellerstrand, hakank@gmail.com % See also http://www.hakank.org/answer_set_programming/ % % Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ % r:red, g:green % y:yello, ry: red-yellow % cars(r;g;ry;y). pedestrians(r;g). ix(1..4). allowed(r,r,g,g). allowed(ry,r,y,r). allowed(g,g,r,r). allowed(y,r,ry,r). % cars 1 { v(Ix, Car) : cars(Car) } 1 :- ix(Ix). % pedestrians 1 { p(Ix, Pedestrian) : pedestrians(Pedestrian) } 1 :- ix(Ix). :- ix(I), ix(J), J == (1+I) \ 4, v(I, VI), v(J, VJ), p(I, PI), p(J,PJ), not allowed(VI,PI,VJ,PJ). % combined for #show all(V1,P1,V2,P2,V3,P3,V4,P4) :- v(1,V1), v(2,V2), v(3,V3),v(4,V4), p(1,P1), p(2,P2), p(3,P3),p(4,P4). % #show v/2. % #show p/2. #show all/8.