SYNOPSIS

lpo2lts-sym [OPTION]… file.tbf [outfile.etf]

DESCRIPTION

lpo2lts-sym performs a reachability analysis on a specification provided in file.tbf. Specifications are in tbf format and are commonly generated by mcrl(1) or mcrl22mcrl(1). outfile.etf specifies the name of the output archive, written in etf(5) format.

OPTIONS

--order=ORDER

Select the exploration strategy: bfs-prev, bfs, chain-prev, or chain. With bfs-prev and bfs, breadth-first search is used. Here, bfs-prev only considers the states found at the previous level, while bfs considers the whole visited set. With chain-prev and chain, a chaining strategy is used. Here, chain-prev at each level starts from the states found at the previous level, while chain uses the whole visited set. Defaults to bfs-prev.

When using breadth-first search, the tool performs the next state computation for all edge groups on the current level or current set of visited states. Chaining means to apply next state for the first group to the visited states, then apply next-state for the second group to the result, etc. Thus, a chaining analysis can be completed in much less iterations than a BFS analysis.

--saturation=SATURATION

Select a saturation strategy: none, sat-like, sat-loop, sat-fix, sat. The sat-like strategy goes up and down the levels of the BDD used to represent the state space. The sat-loop strategy loops over the levels. The sat-fix strategy repeatedly performs a fixpoint computation using saturation. The sat strategy does saturation as described in the literature with on-the-fly expansion of the transition relations. Defaults to none, i.e. no saturation.

All strategies except sat-fix and sat work in combination with the order to saturate levels.

--sat-granularity=GRANULARITY

Select the granularity of sat-like and sat-loop strategies. The granularity indicates how many BDD levels are considered at the same time. Defaults to 10.

--save-sat-levels

Save the previous states seen at saturation levels. This option has effect for any of the saturation strategies in combination with either bfs-prev or chain-prev.

--guidance=STRATEGY

Select a search strategy for searching for actions: unguided, directed. The unguided strategy considers all transition groups. The directed strategy focuses the search on the transition groups in which the action occurs. Defaults to unguided.

--dot=DIR

If this option is supplied DIR is a directory to which dot files of vector sets are written to. Note that this option should only be used for smaller vector sets because of disk space.

Three type of dot files are (over)written:

  1. current-l<L>.dot: the nodes in the vector set at level L (and only level L),

  2. visited-l<L>.dot: the nodes in the vector set up to and included level L,

  3. group_next-l<L>-k<K>.dot: the nodes in the transition relation of group K at level L.

--mu=MUFILE|MUFORMULA

After computing all reachable states, evaluate the mu-formula in MUFILE

MUFILE is a file containing a Mu Calculus formula (see ltsmin-mu(5)). Alternatively, the formula can be provide directly as MUFORMULA. This formula is a propositional formula with least and greatest fixpoint operator. It will be evaluated after generation of the complete state space.

--ctl-star=CTLFILE|CTLFORMULA

CTLFILE is a file containing an Linear Temporal Logic Star (CTL*) formula (see ltsmin-ctl(5)). Which content can also be provided directly as CTLFORMULA. The formula is translated to a mu-formula (see ltsmin-mu(5)), which is evaluated after computing all reachable states.

--no-matrix

Do not print the dependency matrix if -v (verbose) is used.

--no-soundness-check

When using --pins-guards=assume-true disable the soundness check of the model specification. The soundness check may be expensive and can be disabled when the model specification is known to be sound. A guard may not evaluate to true or false but to maybe. A guard which evaluates to maybe depends on the evaluation of another guard. For languages such as Promela and DVE it checks whether if a guard evaluates to maybe there is another guard on the left which evaluates to false. For languages such as mCRL2 it also checks whether a guard on the right evaluates to false. If for all states this holds then the model specification is sound for guard-splitting.

--precise

Compute the final number of states precisely.

--next-union

If supported by the vset implementation; perform the computation of successor states simultaneously with unifying the current states. Simultaneously, means with a single BDD/MDD operation.

--inv-par

Checks all invariants in parallel.

--inv-bin-par

Checks both sides of a binary operand in parallel in an invariant, requires --inv-par. Note that this option may actually slow down invariant checking, because parallelization of a binary operand disables short-circuit evaluation.

mCRL Options

--state-names

Make the state parameters visible.

--mcrl=OPTIONS

Pass options to the mcrl(1) library. Defaults to "-alt rw".

Allowed values depend on the mcrl(1) library.

Note
 Some option combinations can lead to incorrect results, e.g., tau confluence when caching is enabled. Therefore, the use of tau confluence has been disabled, but there may be other combinations.
-n, --no-exit

Do not exit when an error is found. Just count errors. Error counts are printed with -v.

-d, --deadlock

Find state with no outgoing transitions. Returns with exit code 1 if a deadlock is found, 0 or 255 (error) otherwise.

-i, --invariant=PREDFILE|PREDEXPRESSION

Find state where the invariant is violated. The file PREDFILE contains an expression in a simple predicate language (see ltsmin-pred(5)). Its contents can also be entered directly as a PREDEXPRESSION. Returns with exit code 1 if a violation is found, 0 or 255 (error) otherwise.

-a, --action=STRING

Find state with an outgoing transition of type STRING. Returns with exit code 1 if the action is found, 0 or 255 (error) otherwise.

--trace='FILE'.gcf

When finding a deadlock state or a transition labelled with a certain action, write a trace to 'FILE'.gcf, beginning from the initial state. Traces can be pretty-printed with ltsmin-printtrace(1).

PINS Options

--labels

Print state variable, type and value names, and state and action labels. Then exit. Useful for writing predicate (--invariant), LTL (--ltl), CTL/CTL* (--ctl), and mu-calculus (--mu) expressions.

--matrix

Print the dependency matrix and exit.

-c, --cache

Enable caching of greybox calls.

If this option is used, the state space generator makes calls to the short version of the greybox next-state function and memoizes the results. If the next-state function is expensive this will yield substantial speedups.

--pins-guards

Use guards in combination with the long next-state function to speed up the next-state function.

--allow-undefined-edges

Allow values for edge variables in atomic predicates to be unreachable.

--allow-undefined-values

Allow undefined values in atomic predicates for enums.

-r, --regroup=SPEC

Enable regrouping optimizations on the dependency matrix.

SPEC is a comma-separated sequence of transformations <(T,)+> which are applied in this order to the dependency matrix. The following transformations T are available:

gs

Group Safely; macro for "gc,gr,cw,rs"; almost always a win.

ga

Group Aggressively (row subsumption); macro for "gc,rs,ru,cw,rs"; can be a huge win, but in some cases causes slower state space generation.

gsa

Group Simulated Annealing; macro for "gc,gr,csa,rs"; almost always a win; usually better than gs.

gc

Group Columns; macro for "cs,cn".

gr

Group Rows; macro for "rs,rn".

cs

Column Sort; sort columns lexicographically.

cn

Column Nub; (temporarily) group duplicate columns, thereby making ca more tractable. Requires cs.

cw

Column sWap; minimize distance between columns by swapping them heuristically. This reordering improves performance of the symbolic data structures.

ca

Column All permutations; try to find the column permutation with the best cost metric. Potentially, this is an expensive operation.

csa

Column Simulated Annealing; minimize distance between columns by swapping them using simulated annealing.

rs

Row Sort; sort rows lexicographically.

rn

Row Nub; remove duplicate rows from the dependency matrix. This is always a win. Requires rs.

ru

Row sUbsume; try to remove more rows than nubbing, thereby trading speed for memory. Requires rs.

w2W

Over-approximate all must-write to may-write. May-write supports the copy (-) dependency.

r2+

Over-approximate read to read+write. Allows read dependencies to also subsume write dependencies.

w2+

Over-approximate must-write to read+write. Allows must-write dependencies to also subsume read dependencies.

W2+

Over-approximate may-write to read+write. Allows must-write dependencies to also subsume read dependencies.

-2r

Over-approximate copy to read. May be useful for testing whether the dependency matrix is correct.

rb4w

Use special heuristics to move read dependencies before write dependences. Often a win in symbolic state space generation.

mm

Writes metrics of the selected (sr, sw, sc) matrix to stdout. The following metrics are printed:

  1. Event span: the total distance between the minimum and maximum column of rows.

  2. Normalized event span: the event span divided by the size of the matrix (rows x columns).

  3. Weighted event span: the weighted event span, the event span, including a moment signifying the location of the span. See, Siminiceanu et al., we use moment 1.

  4. Normalized weighted event span: the weighted event span divided by the size of the matrix (rows x column).

sr

Select the read matrix for cs, csa, cw, ca, rs, bcm, bs, bk, vcm, vacm, vgps and mm.

sw

Select the write matrix (default) for cs, csa, cw, ca, rs, bcm, bs, bk, vcm, vacm, vgps and mm. The write matrix is the default selection, because only write dependencies can create new nodes in decision diagrams. A bad variable order in the write matrix thus leads to a large number of peak nodes during reachability analysis. A bad variable order in the read matrix can also lead to a slow reachability analysis, but typically not as severe as a bad variable order in the write matrix. Slow reachability analysis due to a bad variable order in the read matrix causes many recursive calls to the relational product operation. Typically it is best that read dependencies are moved to the top DD level, thus left most in the read matrix.

sc

Select the combined matrix for cs, csa, cw, ca, rs, bcm, bs, bk, vcm, vacm, vgps and mm. The combined matrix is the logical or of the read and write matrix.

bg

Use a bipartite graph (default) for bcm, bk, bs, vcm, vacm and vgps.

tg

Create a total graph of the bipartite graph for bcm, bk, bs, vcm, vacm and vgps. This adds more vertices and edges thus increasing computation time, but sometimes provides a better ordering.

Below, the sparse matrix algorithms prefixed with b are only available when LTSmin is compiled with Boost. Algorithms prefixed with v are only available when LTSmin is compiled with ViennaCL.

bcm

Apply Boost’s Cuthill-McKee ordering.

bk

Apply Boost’s King ordering.

bs

Apply Boost’s Sloan ordering.

vcm

Apply ViennaCL’s Cuthill-McKee ordering.

vacm

Apply ViennaCL’s advanced Cuthill-McKee ordering.

vgps

Apply ViennaCl’s Gibbs-Poole-Stockmeyer ordering.

f

Apply FORCE ordering.

--row-perm=PERM

Apply row permutation PERM, where PERM is a sequence of row numbers, separated by a comma. E.g. the vector 2,1,0 will swap row 2 with row 0.

--col-perm=PERM

Apply column permutation PERM, where PERM is a sequence of column numbers, separated by a comma. E.g. the vector 2,1,0 will swap column 2 with column 0.

--col-ins=PAIRS

Insert columns before other columns in the dependency matrix.

PAIRS is a comma-separated sequence of pairs <(C.C,)+>'. E.g. --col-ins=1.0 will insert column 1 before column 0. Each pair contains a source column C and a target column C'. During the application of the whole sequence, C will always be the column number that corresponds with the column before the application of the whole sequence. The column number C' will always be the column during the application of the whole sequence. This means that in for example --col-ins=2.0,1.0, first column 2 is inserted at position 0, then column 1 is inserted at position 0. The result will be that the original column 2 will be at position 1. Another important detail is that when --col-ins is used, all source columns will temporarily be "removed" during reordering from the dependency matrix, i.e. when the -r,--regroup option is given. After reordering is done, the columns will be inserted at the desired target position. In other words, reordering algorithms given by the option -r,--regroup, will only be applied on the dependency matrix with source columns removed.

--sloan-w1=WEIGHT1

Use WEIGHT1 as the first weight for the Sloan algorithm, see https://www.boost.org/doc/libs/1_66_0/libs/graph/doc/sloan_ordering.htm.

--sloan-w2=WEIGHT2

Use WEIGHT2 as the second weight for the Sloan algorithm, see https://www.boost.org/doc/libs/1_66_0/libs/graph/doc/sloan_ordering.htm.

--graph-metrics

Print Boost’s and ViennaCL’s graph metrics (only available when LTSmin is compiled with Boost or ViennaCL).

--regroup-exit

Exit with 0 when regrouping is done.

--regroup-time

Print timing information of each transformation, given in sequence --regroup (-r).

--mucalc=FILE|FORMULA

Compute a parity game for the mu-calculus formula.

The mu-calculus formula is provided in the file FILE or directly as a string FORMULA. The syntax and tool support are described in ltsmin-mucalc(5).

--por=heur|del

Activate partial-order reduction

Partial-Order Reduction (POR) can reduce the state space when searching for deadlocks (-d) or accepting cycles (--ltl). Two POR algorithms are available:

heur

Uses a cost-based heuristic beam-search to find the smallest stubborn set

del

Uses Valmari’s deletion algorithm to find the smallest stubborn set by iteratively removing transitions while maintaining the constraints.

--weak

Use weak commutativity in partial-order reduction. Possibly yielding better reductions.

--leap

Use leaping partial-order reduction, by combining several disjoint stubborn sets sequentially.

Environment Variables

LTSmin supports the following list of environment variables.

Table 1. Environment Variables:
Name Unit Description

LTSMIN_MEM_SIZE

bytes

Sets the amount of system memory to the given value.

LTSMIN_NUM_CPUS

constant

Sets the amount of CPUs to the given value.

The variables LTSMIN_MEM_SIZE, and LTSMIN_NUM_CPUS are particularly relevant when neither sysconf(3) nor cgroups(7) is able to properly detect these limits, e.g. when LTSmin runs on Travis CI in a docker container.

Symbolic Parity Game Options

A symbolic parity game can be generated either by using the --mucalc option or by using the PBES language module.

--pg-solve

Solve the generated parity game.

--pg-reduce

Reduce the generated parity game on-the-fly (experimental).

--pg-write=FILE

Writes a symbolic parity game to FILE.

Symbolic Parity Game Solver Options

--attr=default|chain|par|par2

Choose attractor function.

Available attractor functions:

default

Straightforward attractor computation.

chain

Chaining attractor, applies transition groups in a different order than default in computing an attractor level.

par

Spawns parallel tasks to compute forward and backward steps for each attractor level.

par2

Spawns more parallel tasks than par, by applying forward steps in parallel to the result of the backward steps of the different transition groups.

--saturating-attractor

Use saturation in the chaining attractor.

--pg-write-dot

Write dot files to disk during parity game solving for debugging.

Vector Set Options

--vset=TYPE

Select type of vector set: ldd64, ldd, list, tree, fdd, ddd, sylvan, or lddmc. With ldd64, the 64-bit ListDD list encoding is used (non-ATerm based). With ldd, the 32-bit ListDD list encoding is used (non-ATerm based). With list, ATermDD with list encoding is used. With tree, ATermDD with tree encoding is used. With fdd, BuDDy FDDs are used. With ddd, libDDD SDDs are used. With sylvan, the parallel BDD package Sylvan is used. With lddmc, the parallel LDD package LDDmc is used. Defaults to first available type in the list.

vset-cache-diff=diff

Influences the size of operations cache when counting precisely with bignums: cache size = floor((2log(nodes-to-count) + <diff>)^2). More precisely; LTSmin will bitshift <diff> bits to the left or right on the number of nodes in the vector set, depending on the signedness of <diff>. The default is 0, meaning that if the cache is full the number of bignums in memory will be equal to the number of nodes in the vector set. The default value seems to work well, even when the number vectors in the vector set is very large relative to the number of nodes. If the number of vectors relative to the number of nodes is lower, <diff> may be decreased. The user may want to set <diff> as low as possible (to save memory), while keeping the operations cache effective. Bignums are not floating point numbers and may thus consume a lot of memory.

ListDD Options

--ldd32-step=STEP

The internal tables of ListDD resize according to the Fibonacci series. This option sets the initial size to the Fibonacci number STEP. Defaults to 30.

--ldd32-cache=DIFF

Set Fibonacci difference DIFF between the cache and nodes (DIFF may be negative). Defaults to 1.

ListDD Options

--ldd-step=STEP

The internal tables of ListDD resize according to the Fibonacci series. This option sets the initial size to the Fibonacci number STEP. Defaults to 30.

--ldd-cache=DIFF

Set Fibonacci difference DIFF between the cache and nodes (DIFF may be negative). Defaults to 1.

BuDDy Options

--cache-ratio=RATIO

Set cache ration. Defaults to 64.

--max-increase=NUMBER

Set maximum increase. Defaults to 1,000,000.

--min-free-nodes=PERCENTAGE

Sets the minimum percentage of free nodes as integer between 0 and 100. Defaults to 20.

--fdd-bits=BITS

Sets the number of bits for each FDD variable. Defaults to 16.

--fdd-reorder=STRATEGY

Sets the strategy for dynamic variable reordering. Valid options are none, win2, win2ite, win3, win3ite, sift, siftite, random. Refer to the BuDDy manual for details. Defaults to none.

Sylvan Options

--sylvan-threads=NUMBER

Set number of workers. Defaults to 1.

*--sylvan-dqsize Sets the size of the (static) task queue for work stealing in Wool to N. Defaults to 100000.

--sylvan-tablesize=NUMBER

Sets the size of the BDD table to 1<<N nodes. Defaults to 23. Maximum of 29.

--sylvan-cachesize=NUMBER

Set the size of the memoization table to 1<<N entries. Defaults to 23.

--sylvan-bits=BITS

Sets the number of bits for each integer in the state vector. Defaults to 16.

--sylvan-granularity=NUMBER

Controls memoization table usage. Only use the memoization table every 1/N BDD levels. Defaults to 1, i.e., always use the table.

LDDmc Options

--lddmc-tablesize=NUMBER

Sets the size of the BDD table to 1<<N nodes. Defaults to 23. Maximum of 29.

--lddmc-cachesize=NUMBER

Set the size of the memoization table to 1<<N entries. Defaults to 23.

Lace Options

--lace-workers=NUMBER

Set number of Lace workers (threads for parallelization). Defaults to the number of available cores if parallel algorithms are used, 1 otherwise.

--lace-dqsize=NUMBER

Set length of Lace task queue. Defaults to 40960000.

--lace-stacksize=NUMBER

Set size of program stack in kilo bytes. Defaults to 0, which means using the default stack size.

General Options

-v

Increase the level of verbosity

-q

Be quiet; do not print anything to the terminal.

--debug=<file.c>

Enable debugging output for file.c (option allowed multiple times).

--version

Print version string of this tool.

-h, --help

Print help text

--usage

Print short usage summary.

EXIT STATUS

0

Successful termination.

1

Counter example found.

255

Some error occurred.

SUPPORT

Send questions, bug reports, comments and feature suggestions to the LTSmin Support Team.

SEE ALSO

ltsmin(7), etf(5), ltsmin-mpi(1), ltsmin-mucalc(5), ltsmin-convert(1), ltsmin-printtrace(1), ICTAC 2008, LNCS 5160, muCRL, mCRL2, DiVinE 2.2, MPI Forum, BuDDy, prom, and ProB