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_This document is best viewed in ["raw format" on github](https://raw.githubusercontent.com/CinRC/IRDC-CCSK/master/docs/lts.md)._ | ||
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The LTS (labelled transition system, or SOS, for structural operational semantics) of CSSK is the set of "reduction | ||
rules" describing how the system reacts / evolves. | ||
It is given, for instance, in _Forward-Reverse Observational Equivalences in CCSK_ (page 4, for the forward-only system) | ||
, or [in this exercise sheet](https://github.com/CinRC/Exercises-on-CCS-CCSK-and-RCCS/blob/master/exercises_2/main.pdf). | ||
The LTS (labelled transition system, or SOS, for structural operational semantics) of CSSK is the set of "reduction rules" describing how the system reacts / evolves. | ||
It is given, for instance, in _Forward-Reverse Observational Equivalences in CCSK_ (page 4, for the forward-only system), or [in this exercise sheet](https://github.com/CinRC/Exercises-on-CCS-CCSK-and-RCCS/blob/master/exercises_2/main.pdf). | ||
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For simplification, we have written these rules down in 'ascii' format. | ||
They are as follows: | ||
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+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| Rule | Example(s) | | ||
| Rule | Example(s) | | ||
+:=============================================:+:===================================================================:+ | ||
|``` | - `a.P -a[k0]-> a[k0].P` | | ||
| | - `a.b.P -a[k0]-> a[k0].b.P` | | ||
| | | | ||
| std(X)------------------ (top) | | | ||
| a.X -a[m]-> a[m].X | | | ||
| | | | ||
| | | | ||
|``` | | | ||
|``` | - `a.P -a[k0]-> a[k0].P` | | ||
| | - `a.b.P -a[k0]-> a[k0].b.P` | | ||
| | | | ||
| std(X)------------------ (top) | | | ||
| a.X -a[m]-> a[m].X | | | ||
| | | | ||
| | | | ||
|``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
|``` | - `a[k0].b.P -b[k1]-> a[k0].b[k1].P` | | ||
| | - `a[k0].(b.X|Y) -b[k1]-> a[k0].(b[k1].X|Y)` | | ||
| | | | ||
| X -b[n]-> X' | | | ||
| m neq n------------------------ (pre.) | | | ||
| a[m].X -b[n]-> a[m].X' | | | ||
| | | | ||
| | | | ||
|``` | | | ||
| | - `a[k0].(b.X|Y) -b[k1]-> a[k0].(b[k1].X|Y)` | | ||
| | | | ||
| X -b[n]-> X' | | | ||
| m neq n------------------------ (pre.) | | | ||
| a[m].X -b[n]-> a[m].X' | | | ||
| | | | ||
| | | | ||
|``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| ``` | - `a.P\{b} -a[k0]-> a[k0].P\{b}` | | ||
| | | | ||
| | | | ||
| X -z[m]-> X' | | | ||
| z notin {a, 'a} --------------------- (res.) | | | ||
| X\{a} -z[m]-> X'\{a} | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
| | | | ||
| | | | ||
| X -z[m]-> X' | | | ||
| z notin {a, 'a} --------------------- (res.) | | | ||
| X\{a} -z[m]-> X'\{a} | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| ``` | - `a.P|b.Q -a[k0]-> a[k0].P|b.Q` | | ||
| | | | ||
| | | | ||
| X -a[m]-> X' | | | ||
| m notin keys(Y)-------------------- (|L) | | | ||
| X|Y -a[m]-> X'|Y | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
| | | | ||
| | | | ||
| X -a[m]-> X' | | | ||
| m notin keys(Y)-------------------- (|L) | | | ||
| X|Y -a[m]-> X'|Y | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| ``` | - `a.P|b.Q -b[k0]-> a.P|b[k0].Q` | | ||
| | | | ||
| | | | ||
| Y -a[m]-> Y' | | | ||
| m notin keys(X)-------------------- (|R) | | | ||
| X|Y -a[m]-> X|Y' | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
| | | | ||
| | | | ||
| Y -a[m]-> Y' | | | ||
| m notin keys(X)-------------------- (|R) | | | ||
| X|Y -a[m]-> X|Y' | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| ``` | - `a.P + b.Q -a[k0]-> a[k0].P + b.Q` | | ||
| | | | ||
| | | | ||
| X -a[m]-> X' | | | ||
| std(Y)------------------------ (+L) | | | ||
| X+Y -a[m]-> X'+Y | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
| | | | ||
| | | | ||
| X -a[m]-> X' | | | ||
| std(Y)------------------------ (+L) | | | ||
| X+Y -a[m]-> X'+Y | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| ``` | - `a.P + b.Q -b[k0]-> a.P + b[k0].Q` | | ||
| | | | ||
| | | | ||
| Y -a[m]-> Y' | | | ||
| std(X)------------------------ (+R) | | | ||
| X+Y -a[m]-> X+Y' | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
| | | | ||
| | | | ||
| Y -a[m]-> Y' | | | ||
| std(X)------------------------ (+R) | | | ||
| X+Y -a[m]-> X+Y' | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ | ||
| ``` | - `a.P|'a.Q -Tau{a,'a}[k0]-> Tau{a,'a}[k0].P|Tau{a,'a}[k0].Q` | | ||
| | | | ||
| | | | ||
| X -a[m]-> X' Y -'a[m]-> Y' | | | ||
| -------------------------------- (syn.) | | | ||
| X|Y -Tau{a,'a}[m]-> X'|Y' | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
| | | | ||
| | | | ||
| X -a[m]-> X' Y -'a[m]-> Y' | | | ||
| -------------------------------- (syn.) | | | ||
| X|Y -Tau{a,'a}[m]-> X'|Y' | | | ||
| | | | ||
| | | | ||
| ``` | | | ||
+-----------------------------------------------+---------------------------------------------------------------------+ |
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