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			examples and small fix regarding changes of elimination model checker
			
				
		examples and small fix regarding changes of elimination model checker
	
		
	
			
				Former-commit-id: 2cc4247372
			
			
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				 6 changed files with 456 additions and 5 deletions
			
			
		- 
					176examples/pmdp/firewire/firewire.nm
- 
					4examples/pmdp/firewire/firewire.prop
- 
					258examples/pmdp/zeroconf/zeroconf.nm
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					2examples/pmdp/zeroconf/zeroconf.prop
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					9src/modelchecker/reachability/SparseDtmcEliminationModelChecker.h
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					12src/modelchecker/region/SparseDtmcRegionModelChecker.cpp
| @ -0,0 +1,176 @@ | |||||
|  | // firewire protocol with integer semantics | ||||
|  | // dxp/gxn 14/06/01 | ||||
|  | 
 | ||||
|  | // CLOCKS | ||||
|  | // x1 (x2) clock for node1 (node2) | ||||
|  | // y1 and y2 (z1 and z2) clocks for wire12 (wire21) | ||||
|  | 
 | ||||
|  | mdp | ||||
|  | 
 | ||||
|  | // maximum and minimum delays | ||||
|  | // fast | ||||
|  | const int rc_fast_max = 85; | ||||
|  | const int rc_fast_min = 76; | ||||
|  | // slow | ||||
|  | const int rc_slow_max = 167; | ||||
|  | const int rc_slow_min = 159; | ||||
|  | // delay caused by the wire length | ||||
|  | const int delay; | ||||
|  | // probability of choosing fast | ||||
|  | const double fast1; // = 0.5; | ||||
|  | const double slow1=1-fast1; | ||||
|  | const double fast2; // = 0.5; | ||||
|  | const double slow2=1-fast2; | ||||
|  | 
 | ||||
|  | module wire12 | ||||
|  | 	 | ||||
|  | 	// local state | ||||
|  | 	w12 : [0..9]; | ||||
|  | 	// 0 - empty | ||||
|  | 	// 1 -	rec_req | ||||
|  | 	// 2 -  rec_req_ack | ||||
|  | 	// 3 -	rec_ack | ||||
|  | 	// 4 -	rec_ack_idle | ||||
|  | 	// 5 -	rec_idle | ||||
|  | 	// 6 -	rec_idle_req | ||||
|  | 	// 7 -	rec_ack_req | ||||
|  | 	// 8 -	rec_req_idle | ||||
|  | 	// 9 -	rec_idle_ack | ||||
|  | 	 | ||||
|  | 	// clock for wire12 | ||||
|  | 	y1 : [0..delay+1]; | ||||
|  | 	y2 : [0..delay+1]; | ||||
|  | 
 | ||||
|  | 	// empty | ||||
|  | 	// do not need y1 and y2 to increase as always reset when this state is left | ||||
|  | 	// similarly can reset y1 and y2 when we re-enter this state | ||||
|  | 	[snd_req12]  w12=0 -> (w12'=1) & (y1'=0) & (y2'=0); | ||||
|  | 	[snd_ack12]  w12=0 -> (w12'=3) & (y1'=0) & (y2'=0); | ||||
|  | 	[snd_idle12] w12=0 -> (w12'=5) & (y1'=0) & (y2'=0); | ||||
|  | 	[time]       w12=0 -> (w12'=w12);	 | ||||
|  | 	// rec_req | ||||
|  | 	[snd_req12]  w12=1 -> (w12'=1); | ||||
|  | 	[rec_req12]  w12=1 -> (w12'=0) & (y1'=0) & (y2'=0); | ||||
|  | 	[snd_ack12]  w12=1 -> (w12'=2) & (y2'=0); | ||||
|  | 	[snd_idle12] w12=1 -> (w12'=8) & (y2'=0); | ||||
|  | 	[time]       w12=1 & y2<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_req_ack | ||||
|  | 	[snd_ack12] w12=2 -> (w12'=2); | ||||
|  | 	[rec_req12] w12=2 -> (w12'=3); | ||||
|  | 	[time]      w12=2 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_ack | ||||
|  | 	[snd_ack12]  w12=3 -> (w12'=3); | ||||
|  | 	[rec_ack12]  w12=3 -> (w12'=0) & (y1'=0) & (y2'=0); | ||||
|  | 	[snd_idle12] w12=3 -> (w12'=4) & (y2'=0); | ||||
|  | 	[snd_req12]  w12=3 -> (w12'=7) & (y2'=0); | ||||
|  | 	[time]       w12=3 & y2<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_ack_idle | ||||
|  | 	[snd_idle12] w12=4 -> (w12'=4); | ||||
|  | 	[rec_ack12]  w12=4 -> (w12'=5); | ||||
|  | 	[time]       w12=4 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_idle | ||||
|  | 	[snd_idle12] w12=5 -> (w12'=5); | ||||
|  | 	[rec_idle12] w12=5 -> (w12'=0) & (y1'=0) & (y2'=0); | ||||
|  | 	[snd_req12]  w12=5 -> (w12'=6) & (y2'=0); | ||||
|  | 	[snd_ack12]  w12=5 -> (w12'=9) & (y2'=0); | ||||
|  | 	[time]       w12=5 & y2<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_idle_req | ||||
|  | 	[snd_req12]  w12=6 -> (w12'=6); | ||||
|  | 	[rec_idle12] w12=6 -> (w12'=1); | ||||
|  | 	[time]       w12=6 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_ack_req | ||||
|  | 	[snd_req12] w12=7 -> (w12'=7); | ||||
|  | 	[rec_ack12] w12=7 -> (w12'=1); | ||||
|  | 	[time]      w12=7 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_req_idle | ||||
|  | 	[snd_idle12] w12=8 -> (w12'=8); | ||||
|  | 	[rec_req12]  w12=8 -> (w12'=5); | ||||
|  | 	[time]       w12=8 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	// rec_idle_ack | ||||
|  | 	[snd_ack12]  w12=9 -> (w12'=9); | ||||
|  | 	[rec_idle12] w12=9 -> (w12'=3); | ||||
|  | 	[time]       w12=9 & y1<delay ->  (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); | ||||
|  | 	 | ||||
|  | endmodule | ||||
|  | 
 | ||||
|  | module node1 | ||||
|  | 	 | ||||
|  | 	// clock for node1 | ||||
|  | 	x1 : [0..168]; | ||||
|  | 	 | ||||
|  | 	// local state | ||||
|  | 	s1 : [0..8]; | ||||
|  | 	// 0 - root contention | ||||
|  | 	// 1 - rec_idle | ||||
|  | 	// 2 - rec_req_fast | ||||
|  | 	// 3 - rec_req_slow | ||||
|  | 	// 4 - rec_idle_fast | ||||
|  | 	// 5 - rec_idle_slow | ||||
|  | 	// 6 - snd_req | ||||
|  | 	// 7- almost_root | ||||
|  | 	// 8 - almost_child | ||||
|  | 	 | ||||
|  | 	// added resets to x1 when not considered again until after rest | ||||
|  | 	// removed root and child (using almost root and almost child) | ||||
|  | 	 | ||||
|  | 	// root contention immediate state) | ||||
|  | 	[snd_idle12] s1=0 -> fast1 : (s1'=2) & (x1'=0) +  slow1 : (s1'=3) & (x1'=0); | ||||
|  | 	[rec_idle21] s1=0 -> (s1'=1); | ||||
|  | 	// rec_idle immediate state) | ||||
|  | 	[snd_idle12] s1=1 -> fast1 : (s1'=4) & (x1'=0) +  slow1 : (s1'=5) & (x1'=0); | ||||
|  | 	[rec_req21]  s1=1 -> (s1'=0); | ||||
|  | 	// rec_req_fast | ||||
|  | 	[rec_idle21] s1=2 -> (s1'=4);	 | ||||
|  | 	[snd_ack12]  s1=2 & x1>=rc_fast_min -> (s1'=7) & (x1'=0); | ||||
|  | 	[time]       s1=2 & x1<rc_fast_max -> (x1'=min(x1+1,168)); | ||||
|  | 	// rec_req_slow | ||||
|  | 	[rec_idle21] s1=3 -> (s1'=5); | ||||
|  | 	[snd_ack12]  s1=3 & x1>=rc_slow_min -> (s1'=7) & (x1'=0); | ||||
|  | 	[time]       s1=3 & x1<rc_slow_max -> (x1'=min(x1+1,168)); | ||||
|  | 	// rec_idle_fast | ||||
|  | 	[rec_req21] s1=4 -> (s1'=2); | ||||
|  | 	[snd_req12] s1=4 & x1>=rc_fast_min -> (s1'=6) & (x1'=0); | ||||
|  | 	[time]      s1=4 & x1<rc_fast_max -> (x1'=min(x1+1,168)); | ||||
|  | 	// rec_idle_slow | ||||
|  | 	[rec_req21] s1=5 -> (s1'=3); | ||||
|  | 	[snd_req12] s1=5 & x1>=rc_slow_min -> (s1'=6) & (x1'=0); | ||||
|  | 	[time]      s1=5 & x1<rc_slow_max -> (x1'=min(x1+1,168)); | ||||
|  | 	// snd_req  | ||||
|  | 	// do not use x1 until reset (in state 0 or in state 1) so do not need to increase x1 | ||||
|  | 	// also can set x1 to 0 upon entering this state | ||||
|  | 	[rec_req21] s1=6 -> (s1'=0); | ||||
|  | 	[rec_ack21] s1=6 -> (s1'=8); | ||||
|  | 	[time]      s1=6 -> (s1'=s1); | ||||
|  | 	// almost root (immediate)  | ||||
|  | 	// loop in final states to remove deadlock | ||||
|  | 	[] s1=7 & s2=8 -> (s1'=s1); | ||||
|  | 	[] s1=8 & s2=7 -> (s1'=s1); | ||||
|  | 	[time] s1=7 -> (s1'=s1); | ||||
|  | 	[time] s1=8 -> (s1'=s1); | ||||
|  | 	 | ||||
|  | endmodule | ||||
|  | 
 | ||||
|  | // construct remaining automata through renaming | ||||
|  | module wire21=wire12[w12=w21, y1=z1, y2=z2,  | ||||
|  | 	snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21, | ||||
|  | 	rec_req12=rec_req21, rec_idle12=rec_idle21, rec_ack12=rec_ack21] | ||||
|  | endmodule | ||||
|  | module node2=node1[s1=s2, s2=s1, x1=x2, fast1=fast2, slow1=slow2, | ||||
|  | 	rec_req21=rec_req12, rec_idle21=rec_idle12, rec_ack21=rec_ack12, | ||||
|  | 	snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21] | ||||
|  | endmodule | ||||
|  | 
 | ||||
|  | // labels | ||||
|  | label "done" = (s1=8 & s2=7) | (s1=7 & s2=8); | ||||
|  | 
 | ||||
|  | // reward structures | ||||
|  | 
 | ||||
|  | // time | ||||
|  | rewards "time"	 | ||||
|  | 	[time] true : 1; | ||||
|  | endrewards | ||||
|  | 
 | ||||
|  | // time nodes sending | ||||
|  | rewards "time_sending" | ||||
|  | 	[time] (w12>0 | w21>0) : 1; | ||||
|  | endrewards | ||||
| @ -0,0 +1,4 @@ | |||||
|  | Pmin=?[ F (s1=8 & s2=7) ] | ||||
|  | //R{"time"}min=? [ F "done" ] | ||||
|  | //R{"time"}max=? [ F "done" ] | ||||
|  | //R{"time_sending"}max=? [ F "done" ] | ||||
| @ -0,0 +1,258 @@ | |||||
|  | // IPv4: PTA model with digitial clocks | ||||
|  | // one concrete host attempting to choose an ip address  | ||||
|  | // when a number of (abstract) hosts have already got ip addresses | ||||
|  | // gxn/dxp/jzs 02/05/03 | ||||
|  | 
 | ||||
|  | // model is an mdp | ||||
|  | mdp | ||||
|  | 
 | ||||
|  | // reset or noreset model | ||||
|  | const bool reset=false; | ||||
|  | 
 | ||||
|  | //------------------------------------------------------------- | ||||
|  | 
 | ||||
|  | // we suppose that | ||||
|  | // - the abstract hosts have already picked their addresses  | ||||
|  | //   and always defend their addresses | ||||
|  | // - the concrete host never picks the same ip address twice  | ||||
|  | //   (this can happen only with a verys small probability) | ||||
|  | 
 | ||||
|  | // under these assumptions we do not need message types because: | ||||
|  | // 1) since messages to the concrete host will never be a probe,  | ||||
|  | //    this host will react to all messages in the same way | ||||
|  | // 2) since the abstract hosts always defend their addresses,  | ||||
|  | //    all messages from the host will get an arp reply if the ip matches | ||||
|  | 
 | ||||
|  | // following from the above assumptions we require only three abstract IP addresses | ||||
|  | // (0,1 and 2) which correspond to the following sets of IP addresses: | ||||
|  | 
 | ||||
|  | // 0 - the IP addresses of the abstract hosts which the concrete host  | ||||
|  | //     previously tried to configure | ||||
|  | // 1 - an IP address of an abstract host which the concrete host is  | ||||
|  | //     currently trying to configure | ||||
|  | // 2 - a fresh IP address which the concrete host is currently trying to configure | ||||
|  | 
 | ||||
|  | // if the host picks an address that is being used it may end up picking another ip address | ||||
|  | // in which case there may still be messages corresponding to the old ip address | ||||
|  | // to be sent both from and to the host which the host should now disregard | ||||
|  | // (since it will never pick the same ip address) | ||||
|  | 
 | ||||
|  | // to deal with this situation: when a host picks a new ip address we reconfigure the  | ||||
|  | // messages that are still be be sent or are being sent by changing the ip address to 0  | ||||
|  | // (an old ip address of the host) | ||||
|  | 
 | ||||
|  | // all the messages from the abstract hosts for the 'old' address (in fact the | ||||
|  | // set of old addresses since it may have started again more than once)   | ||||
|  | // can arrive in any order since they are equivalent to the host - it ignores then all | ||||
|  | 
 | ||||
|  | // also the messages for the old and new address will come from different hosts | ||||
|  | // (the ones with that ip address) which we model by allowing them to arrive in any order | ||||
|  | // i.e. not neccessarily in the order they where sent | ||||
|  | 
 | ||||
|  | //------------------------------------------------------------- | ||||
|  | 
 | ||||
|  | 
 | ||||
|  | //------------------------------------------------------------- | ||||
|  | // VARIABLES | ||||
|  | //const int N; // number of abstract hosts | ||||
|  | const int K; // number of probes to send | ||||
|  | const double loss; // probability of message loss | ||||
|  | 
 | ||||
|  | // PROBABILITIES | ||||
|  | const double old; //=N/65024; // probability pick an ip address being used | ||||
|  | const double new = (1-old); // probability pick a new ip address | ||||
|  | 
 | ||||
|  | // TIMING CONSTANTS | ||||
|  | const int CONSEC = 2;  // time interval between sending consecutive probles  | ||||
|  | const int TRANSTIME = 1; // upper bound on transmission time delay | ||||
|  | const int LONGWAIT = 60; // minimum time delay after a high number of address collisions | ||||
|  | const int DEFEND = 10; | ||||
|  | 
 | ||||
|  | const int TIME_MAX_X = 60; // max value of clock x | ||||
|  | const int TIME_MAX_Y = 10; // max value of clock y | ||||
|  | const int TIME_MAX_Z = 1;  // max value of clock z | ||||
|  | 
 | ||||
|  | // OTHER CONSTANTS | ||||
|  | const int MAXCOLL = 10;  // maximum number of collisions before long wait | ||||
|  | // size of buffers for other hosts | ||||
|  | const int B0 = 20;  // buffer size for one abstract host | ||||
|  | const int B1 = 8;  // buffer sizes for all abstract hosts | ||||
|  | 
 | ||||
|  | //------------------------------------------------------------- | ||||
|  | // ENVIRONMENT - models: medium, output buffer of concrete host and all other hosts | ||||
|  | module environment | ||||
|  | 	 | ||||
|  | 	// buffer of concrete host | ||||
|  | 	b_ip7 : [0..2]; // ip address of message in buffer position 8 | ||||
|  | 	b_ip6 : [0..2]; // ip address of message in buffer position 7 | ||||
|  | 	b_ip5 : [0..2]; // ip address of message in buffer position 6 | ||||
|  | 	b_ip4 : [0..2]; // ip address of message in buffer position 5 | ||||
|  | 	b_ip3 : [0..2]; // ip address of message in buffer position 4 | ||||
|  | 	b_ip2 : [0..2]; // ip address of message in buffer position 3 | ||||
|  | 	b_ip1 : [0..2]; // ip address of message in buffer position 2 | ||||
|  | 	b_ip0 : [0..2]; // ip address of message in buffer position 1 | ||||
|  | 	n : [0..8]; // number of places in the buffer used (from host) | ||||
|  | 	 | ||||
|  | 	// messages to be sent from abstract hosts to concrete host | ||||
|  | 	n0  : [0..B0]; // number of messages which do not have the host's current ip address | ||||
|  | 	n1  : [0..B1]; // number of messages which have the host's current ip address | ||||
|  | 	 | ||||
|  | 	b : [0..2]; // local state | ||||
|  | 	// 0 - idle | ||||
|  | 	// 1 - sending message from concrete host  | ||||
|  | 	// 2 - sending message from abstract host | ||||
|  | 	 | ||||
|  | 	z : [0..1]; // clock of environment (needed for the time to send a message) | ||||
|  | 	 | ||||
|  | 	ip_mess : [0..2]; // ip in the current message being sent | ||||
|  | 	// 0 - different from concrete host | ||||
|  | 	// 1 - same as the concrete host and in use | ||||
|  | 	// 2 - same as the concrete host and not in use | ||||
|  | 	 | ||||
|  | 	// RESET/RECONFIG: when host is about to choose new ip address | ||||
|  | 	// suppose that the host cannot choose the same ip address | ||||
|  | 	// (since happens with very small probability).  | ||||
|  | 	// Therefore all messages will have a different ip address,  | ||||
|  | 	// i.e. all n1 messages become n0 ones. | ||||
|  | 	// Note this include any message currently being sent (ip is set to zero 0) | ||||
|  | 	[reset] true -> (n1'=0) & (n0'=min(B0,n0+n1)) // abstract buffers  | ||||
|  | 	               & (ip_mess'=0) // message being set | ||||
|  | 	               & (n'=(reset)?0:n) // concrete buffer (remove this update to get NO_RESET model) | ||||
|  | 	               & (b_ip7'=0)  | ||||
|  | 	               & (b_ip6'=0)  | ||||
|  | 	               & (b_ip5'=0)  | ||||
|  | 	               & (b_ip4'=0)  | ||||
|  | 	               & (b_ip3'=0)  | ||||
|  | 	               & (b_ip2'=0)  | ||||
|  | 	               & (b_ip1'=0)  | ||||
|  | 	               & (b_ip0'=0); | ||||
|  | 	// note: prevent anything else from happening when reconfiguration needs to take place | ||||
|  | 	 | ||||
|  | 	// time passage (only if no messages to send or sending a message) | ||||
|  | 	[time] l>0 & b=0 & n=0 & n0=0 & n1=0 -> (b'=b); // cannot send a message | ||||
|  | 	[time] l>0 & b>0 & z<1 -> (z'=min(z+1,TIME_MAX_Z)); // sending a message | ||||
|  | 	 | ||||
|  | 	// get messages to be sent (so message has same ip address as host) | ||||
|  | 	[send] l>0 & n=0 -> (b_ip0'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=1 -> (b_ip1'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=2 -> (b_ip2'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=3 -> (b_ip3'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=4 -> (b_ip4'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=5 -> (b_ip5'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=6 -> (b_ip6'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=7 -> (b_ip7'=ip) & (n'=n+1); | ||||
|  | 	[send] l>0 & n=8 -> (n'=n); // buffer full so lose message | ||||
|  | 	 | ||||
|  | 	// start sending message from host | ||||
|  | 	[] l>0 & b=0 & n>0 -> (1-loss) : (b'=1) & (ip_mess'=b_ip0)  | ||||
|  | 	                                & (n'=n-1) | ||||
|  | 	                                & (b_ip7'=0)  | ||||
|  | 	                                & (b_ip6'=b_ip7)  | ||||
|  | 	                                & (b_ip5'=b_ip6)  | ||||
|  | 	                                & (b_ip4'=b_ip5)  | ||||
|  | 	                                & (b_ip3'=b_ip4)  | ||||
|  | 	                                & (b_ip2'=b_ip3)  | ||||
|  | 	                                & (b_ip1'=b_ip2)  | ||||
|  | 	                                & (b_ip0'=b_ip1) // send message | ||||
|  | 	                         + loss : (n'=n-1) | ||||
|  | 	                                & (b_ip7'=0)  | ||||
|  | 	                                & (b_ip6'=b_ip7)  | ||||
|  | 	                                & (b_ip5'=b_ip6)  | ||||
|  | 	                                & (b_ip4'=b_ip5)  | ||||
|  | 	                                & (b_ip3'=b_ip4)  | ||||
|  | 	                                & (b_ip2'=b_ip3)  | ||||
|  | 	                                & (b_ip1'=b_ip2)  | ||||
|  | 	                                & (b_ip0'=b_ip1); // lose message | ||||
|  | 	 | ||||
|  | 	// start sending message to host | ||||
|  | 	[] l>0 & b=0 & n0>0 -> (1-loss) : (b'=2) & (ip_mess'=0) & (n0'=n0-1) + loss : (n0'=n0-1); // different ip | ||||
|  | 	[] l>0 & b=0 & n1>0 -> (1-loss) : (b'=2) & (ip_mess'=1) & (n1'=n1-1) + loss : (n1'=n1-1); // same ip | ||||
|  | 	 | ||||
|  | 	// finish sending message from host | ||||
|  | 	[] l>0 & b=1 & ip_mess=0 -> (b'=0) & (z'=0) & (n0'=min(n0+1,B0)) & (ip_mess'=0); | ||||
|  | 	[] l>0 & b=1 & ip_mess=1 -> (b'=0) & (z'=0) & (n1'=min(n1+1,B1)) & (ip_mess'=0); | ||||
|  | 	[] l>0 & b=1 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); | ||||
|  | 	 | ||||
|  | 	// finish sending message to host | ||||
|  | 	[rec] l>0 & b=2 -> (b'=0) & (z'=0) & (ip_mess'=0); | ||||
|  | 	 | ||||
|  | endmodule | ||||
|  | 
 | ||||
|  | //------------------------------------------------------------- | ||||
|  | // CONCRETE HOST | ||||
|  | module host0 | ||||
|  | 	 | ||||
|  | 	x : [0..TIME_MAX_X]; // first clock of the host | ||||
|  | 	y : [0..TIME_MAX_Y]; // second clock of the host | ||||
|  | 	 | ||||
|  | 	coll : [0..MAXCOLL]; // number of address collisions | ||||
|  | 	probes : [0..K]; // counter (number of probes sent) | ||||
|  | 	mess : [0..1]; // need to send a message or not | ||||
|  | 	defend : [0..1]; // defend (if =1, try to defend IP address) | ||||
|  | 	 | ||||
|  | 	ip : [1..2]; // ip address (1 - in use & 2 - fresh) | ||||
|  | 	 | ||||
|  | 	l : [0..4] init 1; // location | ||||
|  | 	// 0 : RECONFIGURE  | ||||
|  | 	// 1 : RANDOM | ||||
|  | 	// 2 : WAITSP | ||||
|  | 	// 3 : WAITSG  | ||||
|  | 	// 4 : USE | ||||
|  | 	 | ||||
|  | 	// RECONFIGURE | ||||
|  | 	[reset] l=0 -> (l'=1); | ||||
|  | 	 | ||||
|  | 	// RANDOM (choose IP address) | ||||
|  | 	[rec] (l=1) -> 1: true; // get message (ignore since have no ip address) | ||||
|  | 	// small number of collisions (choose straight away) | ||||
|  | 	[] l=1 & coll<MAXCOLL -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)  | ||||
|  | 		                     + 1/3*old : (l'=2) & (ip'=1) & (x'=1)  | ||||
|  | 		                     + 1/3*old : (l'=2) & (ip'=1) & (x'=2)  | ||||
|  | 		                     + 1/3*new : (l'=2) & (ip'=2) & (x'=0)  | ||||
|  | 		                     + 1/3*new : (l'=2) & (ip'=2) & (x'=1)  | ||||
|  | 		                     + 1/3*new : (l'=2) & (ip'=2) & (x'=2);  | ||||
|  | 	// large number of collisions: (wait for LONGWAIT) | ||||
|  | 	[time] l=1 & coll=MAXCOLL & x<LONGWAIT -> (x'=min(x+1,TIME_MAX_X)); | ||||
|  | 	[]     l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)  | ||||
|  | 			                                   + 1/3*old : (l'=2) & (ip'=1) & (x'=1)  | ||||
|  | 			                                   + 1/3*old : (l'=2) & (ip'=1) & (x'=2)  | ||||
|  | 			                                   + 1/3*new : (l'=2) & (ip'=2) & (x'=0)  | ||||
|  | 			                                   + 1/3*new : (l'=2) & (ip'=2) & (x'=1)  | ||||
|  | 			                                   + 1/3*new : (l'=2) & (ip'=2) & (x'=2); | ||||
|  | 	 | ||||
|  | 	// WAITSP  | ||||
|  | 	// let time pass | ||||
|  | 	[time]  l=2 & x<2 -> (x'=min(x+1,2)); | ||||
|  | 	// send probe | ||||
|  | 	[send] l=2 & x=2  & probes<K -> (x'=0) & (probes'=probes+1); | ||||
|  | 	// sent K probes and waited 2 seconds | ||||
|  | 	[] l=2 & x=2 & probes=K -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0); | ||||
|  | 	// get message and ip does not match: ignore | ||||
|  | 	[rec] l=2 & ip_mess!=ip -> (l'=l); | ||||
|  | 	// get a message with matching ip: reconfigure | ||||
|  | 	[rec] l=2 & ip_mess=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); | ||||
|  | 	 | ||||
|  | 	// WAITSG (sends two gratuitious arp probes) | ||||
|  | 	// time passage | ||||
|  | 	[time] l=3 & mess=0 & defend=0 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X));  | ||||
|  | 	[time] l=3 & mess=0 & defend=1 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)) & (y'=min(y+1,DEFEND)); | ||||
|  | 	 | ||||
|  | 	// receive message and same ip: defend | ||||
|  | 	[rec] l=3 & mess=0 & ip_mess=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); | ||||
|  | 	// receive message and same ip: defer | ||||
|  | 	[rec] l=3 & mess=0 & ip_mess=ip & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); | ||||
|  | 	// receive message and different ip | ||||
|  | 	[rec] l=3 & mess=0 & ip_mess!=ip -> (l'=l); | ||||
|  | 	 | ||||
|  | 		 | ||||
|  | 	// send probe reply or message for defence | ||||
|  | 	[send] l=3 & mess=1 -> (mess'=0); | ||||
|  | 	// send first gratuitous arp message | ||||
|  | 	[send] l=3 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1); | ||||
|  | 	// send second gratuitous arp message (move to use) | ||||
|  | 	[send] l=3 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); | ||||
|  | 	 | ||||
|  | 	// USE (only interested in reaching this state so do not need to add anything here) | ||||
|  | 	[] l=4 -> 1 : true; | ||||
|  | 	 | ||||
|  | endmodule | ||||
| @ -0,0 +1,2 @@ | |||||
|  | Pmin=? [ F (l=4 & ip=1) ] | ||||
|  | Pmax=? [ F (l=4 & ip=1) ] | ||||
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