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							358 lines
						
					
					
						
							5.9 KiB
						
					
					
				
			
		
		
		
			
			
			
				
					
				
				
					
				
			
		
		
	
	
							358 lines
						
					
					
						
							5.9 KiB
						
					
					
				| { | |
| 	"jani-version": 1, | |
| 	"name": "die.jani", | |
| 	"type": "dtmc", | |
| 	"features": [ "derived-operators" ], | |
| 	"variables": [ | |
| 		{ | |
| 			"name": "s", | |
| 			"type": { | |
| 				"base": "int", | |
| 				"kind": "bounded", | |
| 				"lower-bound": 0, | |
| 				"upper-bound": 7 | |
| 			}, | |
| 			"initial-value": 0 | |
| 		}, | |
| 		{ | |
| 			"name": "d", | |
| 			"type": { | |
| 				"base": "int", | |
| 				"kind": "bounded", | |
| 				"lower-bound": 0, | |
| 				"upper-bound": 6 | |
| 			}, | |
| 			"initial-value": 0 | |
| 		} | |
| 	], | |
| 	"properties": [ | |
| 		{ | |
| 			"name": "Probability to throw a six", | |
| 			"expression": { | |
| 				"op": "filter", | |
| 				"fun": "max", | |
| 				"states": { "op": "initial" }, | |
| 				"values": { | |
| 					"op": "Pmin", | |
| 					"exp": { | |
| 						"op": "U", | |
| 						"left": true, | |
| 						"right": { | |
| 							"op": "∧", | |
| 							"left": { | |
| 								"op": "=", | |
| 								"left": "s", | |
| 								"right": 7 | |
| 							}, | |
| 							"right": { | |
| 								"op": "=", | |
| 								"left": "d", | |
| 								"right": 6 | |
| 							} | |
| 						} | |
| 					} | |
| 				} | |
| 			} | |
| 		}, | |
| 		{ | |
| 			"name": "Expected number of coin flips", | |
| 			"expression": { | |
| 				"op": "filter", | |
| 				"fun": "max", | |
| 				"states": { "op": "initial" }, | |
| 				"values": { | |
| 					"op": "Emin", | |
| 					"accumulate": [ "steps" ], | |
| 					"exp": 1, | |
| 					"reach": { | |
| 						"op": "=", | |
| 						"left": "s", | |
| 						"right": 7 | |
| 					} | |
| 				} | |
| 			} | |
| 		} | |
| 	], | |
| 	"automata": [ | |
| 		{ | |
| 			"name": "die", | |
| 			"locations": [{ "name": "l" }], | |
| 			"initial-locations": ["l"], | |
| 			"edges": [ | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"op": "=", | |
| 							"left": "s", | |
| 							"right": 0 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 1 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 2 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 1 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 3 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 4 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 2 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 5 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 6 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 3 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 },  | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 1 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								}, | |
| 								{ | |
| 									"ref": "d", | |
| 									"value": 1 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 4 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								}, | |
| 								{ | |
| 									"ref": "d", | |
| 									"value": 2 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								}, | |
| 								{ | |
| 									"ref": "d", | |
| 									"value": 3 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 5 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								}, | |
| 								{ | |
| 									"ref": "d", | |
| 									"value": 4 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								}, | |
| 								{ | |
| 									"ref": "d", | |
| 									"value": 5 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 6 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 2 | |
| 								} | |
| 							] | |
| 						}, | |
| 						{ | |
| 							"location": "l", | |
| 							"probability": { "exp": 0.5 }, | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								}, | |
| 								{ | |
| 									"ref": "d", | |
| 									"value": 6 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				}, | |
| 				{ | |
| 					"location": "l", | |
| 					"guard": { | |
| 						"exp": { | |
| 							"left": "s", | |
| 							"op": "=", | |
| 							"right": 7 | |
| 						} | |
| 					}, | |
| 					"destinations": [ | |
| 						{ | |
| 							"location": "l", | |
| 							"assignments": [ | |
| 								{ | |
| 									"ref": "s", | |
| 									"value": 7 | |
| 								} | |
| 							] | |
| 						} | |
| 					] | |
| 				} | |
| 			] | |
| 			 | |
| 		} | |
| 	],  | |
| 	"system": { | |
| 		"elements": [ { "automaton": "die" } ] | |
| 	} | |
| }
 |