A_calculus_for_mobile_network_systems.dvi

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2 +,41,UTC,1?CB3 "ƒ#ƒ#~ $%"$~"#~$##$%#~%x#$( "~ ƒ $ &($'~%#$(Œ %$(~~(~%#ŒŒ"#(" #~"x~(# (x&~ƒ## Šz ~%~~ƒ$&$&##~"( #(&&( # #$~( &ƒ ~% $ #$~( Ž&&ƒ # " ~% ("' r všvp vo r všœ œpžrqÿ pœ ƒ "~~%"(%#( #Œ$ Šz"$( Œ(# ("(Œ( Œ ~&ƒ $~$( Œ(~# %$% $~ ~ƒx~ ~%$( Œ(~# ƒ$% ~%~%" "~({ }{ } "ƒ "~%$("#($( Œ~~( %$( ~%(~%"# $( Œ(~ Šz ƒ %x~~ (x% ("# (# "~(#( #Œ$ Œ ~$( Œ~~( #ƒ$%"((#$( $~( () () ª_«_5/e+,-D/4 +B+?` () ef = α β.0 ef = α (y).y t.0 ef = β (x).0 Ž ~%""("Œ%ƒ#$&&($~(#,,, %#(& &#"Œ"#~ ("~%&($&#ƒ$%"((#"&~(x~ Œ"($### ~%#$#Œ"($## Œ%ƒ#$&#&"$%x&~ƒx~ Œ%ƒ#$&&($~(# ~% (~~ &##~ # # Œ("~ β ~(Œ"($## ~% ##~% Œ("~~(# t~(œ"($## "$%~%#~~ ~"~ (#ƒ$%"( ~(&&(Œ"($####$$##&&ƒ~" ~ ±²³ µ ³ ~" 0 #$% "( Ž ˆ ~(Ž ˆx # # β ~( ~%&($&~(Œ(&(ƒ(~%Œ"($### $% ~%"Œ%ƒ#$& #~"x~(" # ¹º» ±²³ µ ³ ~"Œ"($## (Œ"($####$% "( Ž ˆ ~(Ž ˆ$ ( "~%"&($~(Œ(&(ƒ ( #"( ~( ~%Œ%ƒ#$& #~"x~( ƒ(~x$% ¼ ½¾œ opvp ÀÁšutšt (&&( #~##ƒ~ ~%##$~( (" & Œ&~((("(" & ~( ~#(Œ"~(&# ~$# Â"(" & ~(#x# ~% ~%#~ " ( x#$~~ƒ$(##~#(~ ($( Œ(~# "(Œ(Œ"($### π$&$&# %&~%Œ%ƒ#$& #~"x~(# # ~#( ~"&#~~ Ž(" Œ& {,q} #x#$~~ƒ"œ"#~~( %" Œ"($##(""(Œ(Œ"($### # q #~#Œ%ƒ#$&#~~ %ƒ"x( xƒ Œ"(x"$#

3 ÃWCB6TBTD4/A Ä ~~ƒ$&$&#~%œ%ƒ#$&#œ$# # St %$%$& #&& Œ(##x&Œ%ƒ#$&#~~# Cset #~~# Ž(" Œ&Ž ## ~( Œ"##~%"&~(x~ Œ%ƒ#$& Cset ##Œ$ #(&&( # Cset = {(,),(,),(,),(,),(,),(,),(,),(,),(, ),(, ), ~%$&$&#Œ"&&&# (~ ("&"~ƒ& &##~"~ (,),(,)} $""~&ƒ" #ƒ$%"( ~%"(%Œ%ƒ#$&#~~$(#~" ~~#$( ~( # ~%~~ƒœ"($###"$"" (~Œ"&&& #ƒ$%"( $( $ ~%"(%$( $~($%&# %Œ"($###x( # Œ%ƒ#$&#~~ Å&'(~%"Œ"($##$&$& ~"~Œ%ƒ#$&#~~$~(# ~~ƒ#%"~% %$%Œ~$(#~"~#(~%"#ƒ$%"( ~( %#$(#~"~#" &ƒ #(x#" x&$~(# %Œ%ƒ#$&#~~$~(#$%~%"Œ%ƒ#$&#~~# $& ###$(~x $% $# xƒ~%$~~%~œ%ƒ#$&$( $~(#&#x~%$"""(&( x~ &&(~%Œ%ƒ#$&#~~#~% Œ%ƒ#$&#Œ$ ~%~(~%#~ Æ Ç ²È É ºÊËÇ Ì²³±Í³Í» %Œ"($##&ƒ"#ƒ~ #~%# # Œ%ƒ#$&#~~$~(# ~~ƒ$&$&# Œ"~~(~%$~(#~~(~%" " π$&$&# $Œ~~%~~%$~(#~ t # ~ ~% Œ "$ $~(#~ ~$~(#~# Œ%ƒ#$&#~~$~(#~ St # $~(#~ Cst %~~ƒ&ƒ"#ƒ~ # #(&&( # Crt ~~ƒ$~( ~~%~~ƒ&ƒ"""œ"#~ µ ::= α ( β α x β τ@ β α@ β α ( β α β %Œ"&&&$~(# %" τ@ β α@ β α x # ## ~% &&#~ x α( x) "$ # ## ~%Œ" ~"&#~ x β"œ"#~#~% ~"&#~~(x#$~~ƒ # ~"&$~(x~ ~~# τ@ β x&$~(#(~~ƒ %(" ""Œ"#~#~%~"&$~((x#$ "~ ( "~(x#" ~"&$~(x~ ~ ( ~~ƒ $(~x(x#" ~~%Œ"($##&ƒ" %&~~""Œ"#~#~% ~~ƒ A ::= {,p} A e "~x#$~~# B (x)b e #~~ƒœ"&&&(œ"~(" p # y(#~"~#~ Œ"($##Œ"&&&(Œ"~(" (x)b '#$~( x Cset Cset St St &($&~(~~ƒî ~%#ƒ~ (~%~~ƒ$&$&# $$(" Æ ÏÍ± ÍÏÊÌ Ç ÏÍÊÇ±Ê (Œ"&&&& ~#Œ"($## &ƒ~%œ"($##&ƒ"#~"$~" ~~ƒ" $("$ˆ p ~%Œ"($##&ƒ"#~"$~"$("$#~%# #~%~(~%#~ ~%~~ƒ&ƒ"#~"$~"$("$ˆ e " " π$&$&# %# &&#~~~ƒ&ƒ"#~"$~"$("$# #(&&( # Ð ˆ A e B e B e A ˆ (A e B) e C e A e (B e C) A e {NIL,p} e A; (x)(y)a e (y)(x)a (x)(a e B) e A e (x)b ifx / fn(a)ñ (x){, β} e {(x), β} where β St Ò9,?.11,?+?`6CB6TBTD7?.1A1D?A+6?+/,D/,B`?Ce11Ó16?D/,D1,-,CV1DC,-A Ô,CV1D3 fn(a) A1A1D1,?DCBB?.14A11D1,-C,-A161+01,CV1D/41,?+?`A3

4 Õ +,41,UTC,1?CB3 ˆ {, β} e {, β} where p n β %&#~#~"$~"$("$#%( #~%"&~(x~ ~%Œ"($##&ƒ" St $("$ ~%~~ƒ&ƒ"$("$ ~(&"&#(~%~~ƒ$&$&#"&#($&## Ö ÊÏ² Ç²³»Ê ²Ç ±» z &"~(~%#ƒ~ (~%~~ƒ$&$&#~%(œ" &ƒ"(œ"~(&"&#"x#$&&ƒ~%# #~%(#(~%#~ ~(~ (&ƒ"# %Œ"($## %&~%" ~(&"&# " r1 r2 r3 "~"( $ ~( Œ"##~%"&~( π$&$&# (Œ"($##~"#~(# ~~ƒ~"#~(# r1 : η ;η Cst τ η ;η Crt ; r2 : ; r3 : η ;η St {, β} {, β} {, β} { +, β} {, β} {,η} r2 "$ $~( %#&$~ (~#~%~~%"#( x"$%# ~" ~(# ~" xƒ~#œ%ƒ#$&#~~ ~~ƒ %~### Œ"Ø#Œ%ƒ#$&#~~(~xƒ~#&&(ˆ#"&# ~# ecomm1 %~~ƒ&ƒ"(œ"~(&"&#" #(&&( # Ù ecomm2 A µ A ela : A e B µ A e B ; ea : A µ eb C B e A µ C ; ees : A A ;x η (x)a (x)a ecomm1 : A α@ β A ; {, γ} α@ γ { +, γ} A e {, γ} A e {, γ} if ( β, γ) Cset A α@ β A ; {, γ} α@ γ { +, γ} ecomm2 : A e {, γ} if ( β, γ) / Cset A e {, γ} Ú&# ecomm1 ecomm2 ~(~%" ~% ea #$"x~%œ%ƒ#$& Œ%ƒ#$&#~~# ~%Œ%ƒ#$&#&$x~"#"" #~~$(#~" $( $~( %"#&~(#ƒ$%"( ~( x~ ~ (Œ%ƒ#$& Œ #(~%" #~~#~%Œ"($##~%"$ ~~ƒ(#~(~% ~#~~ Â~%" #~% Œ"($##" #~#("&#~~ Œ%ƒ#$& Š( &~#$%$'~%~"$~(x~ Œ"($###$(# #~"x~(ž %Œ%ƒ#$& ( ~x~ &($~( "~%" ƒ $ ##Œ$ xƒœ"($## ef m ˆm =.. %#ƒ#~ #"Œ"#~ #~%(&&( m System ef = { p m,} e {,} % $~((~%#ƒ#~ # #~%(&&( e {,} ÛÜ16C,TD1ATB1D?.1+AD`VV1?A+6CBATB1D3l/A1fCVB1Ý ela 7eCOMM17eCOMM2?/1?.1A+?. ela?/1?.1a+?. ea ea -1-T61D?/ATB1?/-1-T61 A A eaý µ B µ ea A eb3

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