Benchmark
non-incremental/QF_NRA/20240407-pPDA-Chiari-Pontiggia-Winkler/past/geom_offspring_0.5_PRAY.smt2
Publications:
[1] Tobias Winkler, Joost-Pieter Katoen:
On Certificates, Expected Runtimes, and Termination in Probabilistic Pushdown Automata. LICS 2023: 1-13
This benchmark encodes positive almost sure termination (PAST; termination in finite expected time) of the probabilistic recursive program given below. The program model a process P that spawns a random number of copies of itself; the number of copies is geometrically distributed.
The program was automatically translated to a probabilistic pushdown automaton (pPDA) using the PRAY tool. The SMT formula results from applying Theorem 8 from [1]. The SMT formula is SAT iff the program is PAST.
void P() {
while flip(1//2) {
P();
}
}
P(); # entry point
| Benchmark |
|---|
| Size | 4816 |
| Compressed Size | 1171 |
| License |
Creative Commons Attribution 4.0 International
(CC-BY-4.0)
|
| Category | industrial |
| First Occurrence | 2024-07-22 |
| Generated By | Tobias Winkler |
| Generated On | 2024-04-07 00:00:00 |
| Generator | PRAY - Probabilistic Recursion Analyzer (https://doi.org/10.5281/zenodo.7506305) |
| Dolmen OK | 1 |
| strict Dolmen OK | 1 |
| check-sat calls | 1 |
| Status | unsat |
| Inferred Status | unsat |
| Size | 4808 |
| Compressed Size | 1172 |
| Max. Term Depth | 4 |
| Asserts | 58 |
| Declared Functions | 0 |
| Declared Constants | 29 |
| Declared Sorts | 0 |
| Defined Functions | 0 |
| Defined Recursive Functions | 0 |
| Defined Sorts | 0 |
| Constants | 0 |
| Declared Datatypes | 0 |
Symbols
Evaluations
| Evaluation |
Rating |
Solver |
Variant |
Result |
Wallclock |
CPU Time |
|
SMT-COMP 2024
|
0.20 (4/5) |
cvc5 |
cvc5 |
unsat ✅
|
0.25138
|
0.15213
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.46577
|
0.55377
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.37614
|
0.27646
|
| |
Yices2 |
Yices2 |
unsat ✅
|
0.21914
|
0.11939
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.29577
|
0.19631
|
|
SMT-COMP 2025
|
0.17 (5/6) |
cvc5 |
cvc5 |
unsat ✅
|
0.29783
|
0.18194
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.44873
|
0.49792
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.30355
|
0.18211
|
| |
Yices2 |
Yices2 |
unsat ✅
|
0.28757
|
0.16543
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.62547
|
0.51957
|
| |
Z3 |
Z3-alpha-base |
unsat ✅
|
0.27642
|
0.15765
|
| |
|
z3siri-base |
unsat ✅
|
0.26882
|
0.15212
|