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The composed system RailRoad Systeml (Page 73) has four state variables: east and west, each of which can take two values, and modew and modes, each of which can take three values. Thus, Rail RoadSystem1 has 36 states. How many of these 36 states are reachable? event({arrive, leave}) outw 1 event({arrive, leave}) oute {green, red} west := green; east := green A : west signalw A2 : east signale signalw := west signale := east Az : west, east, oute, outw east, west if oute? leave then west := green; if outw? leave then east := green; if oute ? arrive then west := red else if outw ? arrive then east := red {green, red) signalw {green, red} signale Figure 3.6: A First Attempt at Design of the Railroad Controller west outw oute green arrive arrive red green 1 1 red east modew modes signalw signale green away away green green green wait wait red green wait bridge red green green wait away green green green bridge wait red green green bridge bridge 1 leave green 1 arrive red 1 1 red Figure 3.7: An Execution of RailRoadSystem1 That Violates TrainSafety event({arrive, leave}) outw! event({arrive, leave}) oute {green, red} west := red; east :=red bool nearw := 0; neare := 0 A1 : west signalw A2: east signalg signalw := west signale := east Az : west, east, oute, outw, neare, nearw Heast, west, nearw, neare if oute ? arrive then neare := 1; if oute? leave then neare := 0; if outw? arrive then nearw := = 1; if outw ? leave then nearw := 0; if neare then east := red else if west = red then east := green; if nearw then west := red else if east = red then west := green; {green, red} signalw {green, red} signale Figure 3.8: A Safe Controller for the Railroad Problem The composed system RailRoad Systeml (Page 73) has four state variables: east and west, each of which can take two values, and modew and modes, each of which can take three values. Thus, Rail RoadSystem1 has 36 states. How many of these 36 states are reachable? event({arrive, leave}) outw 1 event({arrive, leave}) oute {green, red} west := green; east := green A : west signalw A2 : east signale signalw := west signale := east Az : west, east, oute, outw east, west if oute? leave then west := green; if outw? leave then east := green; if oute ? arrive then west := red else if outw ? arrive then east := red {green, red) signalw {green, red} signale Figure 3.6: A First Attempt at Design of the Railroad Controller west outw oute green arrive arrive red green 1 1 red east modew modes signalw signale green away away green green green wait wait red green wait bridge red green green wait away green green green bridge wait red green green bridge bridge 1 leave green 1 arrive red 1 1 red Figure 3.7: An Execution of RailRoadSystem1 That Violates TrainSafety event({arrive, leave}) outw! event({arrive, leave}) oute {green, red} west := red; east :=red bool nearw := 0; neare := 0 A1 : west signalw A2: east signalg signalw := west signale := east Az : west, east, oute, outw, neare, nearw Heast, west, nearw, neare if oute ? arrive then neare := 1; if oute? leave then neare := 0; if outw? arrive then nearw := = 1; if outw ? leave then nearw := 0; if neare then east := red else if west = red then east := green; if nearw then west := red else if east = red then west := green; {green, red} signalw {green, red} signale Figure 3.8: A Safe Controller for the Railroad