Benchmark
non-incremental/QF_NRA/20240407-pPDA-Chiari-Pontiggia-Winkler/past/huge_runtime_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; reaching the empty stack in finite expected time) of the probabilistic pushdown automaton (pPDA) from Fig. 4 in [1] with n=10.
Even though the pPDA has only 3 states and 12 stack symbols, it runs approximately 2^(2^n) = 2^1024 steps on average before it reaches the empty stack.
The SMT formula results from applying Theorem 8 from [1] (with equalities instead of inequalities). The SMT formula is SAT iff the automaton is PAST.
| Benchmark |
|---|
| Size | 14483 |
| Compressed Size | 2243 |
| 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 | sat |
| Inferred Status | sat |
| Size | 14475 |
| Compressed Size | 2281 |
| Max. Term Depth | 3 |
| Asserts | 174 |
| Declared Functions | 0 |
| Declared Constants | 87 |
| 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
|
0.60 (2/5) |
cvc5 |
cvc5 |
unknown ❌
|
1201.71957
|
1201.07565
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.57518
|
0.98634
|
| |
SMT-RAT |
SMT-RAT |
unknown ❌
|
1201.77083
|
1201.13502
|
| |
Yices2 |
Yices2 |
sat ✅
|
0.22823
|
0.12862
|
| |
Z3alpha |
Z3-alpha |
sat ✅
|
0.67421
|
0.57489
|
|
SMT-COMP 2025
|
0.50 (3/6) |
cvc5 |
cvc5 |
unknown ❌
|
1201.79343
|
1201.11841
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.55703
|
0.82935
|
| |
SMT-RAT |
SMT-RAT |
unknown ❌
|
1201.48446
|
1201.11451
|
| |
Yices2 |
Yices2 |
sat ✅
|
0.29440
|
0.16906
|
| |
Z3alpha |
Z3-alpha |
sat ✅
|
1.02366
|
2.12543
|
| |
Z3 |
Z3-alpha-base |
sat ✅
|
1.60882
|
1.47721
|
| |
|
z3siri-base |
sat ✅
|
1.69684
|
1.57589
|