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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" } ]
							 | 
						|
									}
							 | 
						|
								}
							 |