German.CTC

Cubicle model

Safety properties

Below are the safety properties we want to verify, in negated form.
Control properties:
∃ z1,z2. z1≠z2 ∧ ( CacheState[z1] = Exclusive ∧ CacheState[z2] ≠ Invalid )

Data properties:
Exgntd = False ∧ MemData ≠ AuxData

∃ z. ( CacheState[z] ≠ Invalid ∧ CacheData[z] ≠ AuxData )

Options used

-brab 2

Inferred invariants

All invariants are shown in their negated form, where #1 and #2 are distinct existentially quantified variables. 

CacheState[#1] = Exclusive && Shrset[#2] = True

Chan2Cmd[#1] = Gnte && Shrset[#2] = True

CacheState[#1] = Exclusive && Invset[#2] = True

Chan2Cmd[#1] = Gnte && Invset[#2] = True

Exgntd = True && Chan2Cmd[#1] = Gnts

Chan2Cmd[#2] = Inv && CacheState[#1] = Exclusive

Chan2Cmd[#1] = Gnte && Chan2Cmd[#2] = Inv

Chan3Cmd[#2] = Invack && CacheState[#1] = Exclusive

Chan2Cmd[#1] = Gnte && Chan3Cmd[#2] = Invack

Chan2Cmd[#1] = Inv && Invset[#1] = True

Chan3Cmd[#1] = Invack && Invset[#1] = True

Curcmd = Empty && Chan2Cmd[#1] = Inv

Chan2Cmd[#1] = Inv && Chan3Cmd[#1] = Invack

Invset[#1] = True && Shrset[#1] = False

Exgntd = False && Curcmd = Reqs && Chan2Cmd[#1] = Inv

Curcmd = Empty && Chan3Cmd[#1] = Invack

Chan2Cmd[#1] = Inv && Shrset[#1] = False

Exgntd = False && Curcmd = Reqs && Chan3Cmd[#1] = Invack

Chan3Cmd[#1] = Invack && Shrset[#1] = False

Chan2Cmd[#1] = Gnts && Chan3Cmd[#1] = Invack

Chan3Cmd[#1] = Invack && CacheState[#1] <> Invalid

Chan2Cmd[#1] = Gnts && Shrset[#1] = False

Chan3Cmd[#1] = Invack && CacheState[#1] = Exclusive

Chan2Cmd[#1] = Gnte && CacheState[#1] = Exclusive

Chan2Cmd[#1] = Gnts && CacheState[#1] = Exclusive

CacheState[#1] <> Invalid && Shrset[#1] = False

Exgntd = False && CacheState[#1] = Exclusive

You can find the list of all invariants that can be extracted from BRAB here (also in negated form), this collection being inductive.

Search graph

The algorithm starts from the formula located at the bottom, inside a red octagon. Variables #1, #2, … that appear in the nodes are distinct skolem variables so we show a formula φ(#1, #2) as equivalent to ∃ z1, z2. z1 ≠ z2 ∧ φ(z1, z2). Plain black edges represent pre-image relations and are annotated by the transition instance that was considered. Black circles denote nodes that were obtained by pre-image computation and were not covered by already visited nodes. The nodes circled in gray are the one that were not useful because they were subsumed by formulas pointed by the gray dashed arrows. Approximations are shown in blue rectangles. Each approximation originates from the node that connects its rectangle with a bold dashed blue edge.