Different TLA+ specifications, mostly for learning purposes

CigaretteSmokers.tla

A specification of the Cigarette smokers problem. The generated state graph is very small:

Blinker.tla

Simple spec simulating, more or less, this application. Three state machines controlling three LEDs. With 100ms resolution (model run with BC <- <<3, 5, 7>>) model checker finds 384 distinct states:

Just a humble reminder to never underestimate even the simplest concurrent programs, I guess 😃

GameOfLife.tla

Conway's Game of Life

All the 'attractors' for a 3x3 grid

State space for a 4x4 grid - original image generated by Graphviz is around 300MB 😃:

The same with some colors based on number of occupied cells:

Zoom on two of the smaller clusters:

Under 'symmetry group of the square' (D₄) view in TLC the state space shrinks to ... 27 states. Under this view it's even possible to run TLC on 5x5 grid and get 486 states (reduction from 33554432):

Base Graphviz parameters:

dot -Tpng -Nstyle=filled -Npenwidth=5 -Epenwidth=8 -Ksfdp -Goverlap=prism -Goverlap_scaling=-10

Requirements.tla

Experimental specification aimed at mechanising verification of written requirements documents.

Checking CheckRequirements spec produces:

SlidingPuzzles.tla

Solution to a variation of sliding block puzzle most commonly known as Klotski.

TLC finds 25955 distinct states. Green node is the starting position. Red nodes are the goal nodes - with the biggest piece in center-bottom position.

The Pennant variation has significantly smaller state space of 'only' 1398 states. Raymond Hettinger talked about this puzzle and the state graph here.

W == 4 H == 5

Pennant == {{<<0, 0>>, <<0, 1>>, <<1, 0>>, <<1, 1>>},
            {<<2, 0>>, <<3, 0>>}, {<<2, 1>>, <<3, 1>>},
            {<<0, 2>>}, {<<1, 2>>},
            {<<0, 3>>, <<0, 4>>}, {<<1, 3>>, <<1, 4>>},
            {<<2, 3>>, <<3, 3>>}, {<<2, 4>>, <<3, 4>>}}
            
PennantGoal == {<<0, 3>>, <<0, 4>>, <<1, 3>>, <<1, 4>>} \in board

Ma's Puzzle has 110804 distinct states.

W == 5 H == 5

Mas == {{<<0, 0>>, <<1, 0>>, <<2, 0>>},
        {<<3, 0>>, <<4, 0>>,<<4, 1>>},
        {<<0, 1>>, <<1, 1>>}, {<<2, 1>>, <<3, 1>>},
        {<<0, 2>>, <<0, 3>>, <<1, 3>>},
        {<<1, 2>>, <<2, 2>>}, {<<3, 2>>, <<4, 2>>},
        {<<2, 3>>, <<3, 3>>, <<4, 3>>},
        {<<2, 4>>}}
        
MasGoal == {{<<3, 0>>, <<4, 0>>,<<4, 1>>}, {<<3, 1>>, <<3, 2>>, <<4, 2>>}} \subseteq board

Chameneos.tla

A specification of a 'concurrency game' requiring concurrent and symmetrical cooperation - link

For N=3 there are 522 distinct states:

The lattices at the edges are due to the possible orders in which the chameneoses fade.

For N=4 there are 6652 distinct states:

All the above graphs are for single initial permutation of chameneoses. Here is a full graph for N=2, M=4 (4843 distinct states).