Benchmark
non-incremental/QF_NRA/20240407-pPDA-Chiari-Pontiggia-Winkler/past/huge_runtime_tiny_probs_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. 3 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. This effect is caused by certain reachability probabilities in the pPDA which are very small, cf. [1].
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 | 10043 |
| Compressed Size | 1878 |
| 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 | 10035 |
| Compressed Size | 1884 |
| Max. Term Depth | 3 |
| Asserts | 140 |
| Declared Functions | 0 |
| Declared Constants | 70 |
| 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 |
sat ✅
|
0.22971
|
0.12998
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.53796
|
0.73433
|
| |
SMT-RAT |
SMT-RAT |
sat ✅
|
0.26176
|
0.16195
|
| |
Yices2 |
Yices2 |
sat ✅
|
0.22082
|
0.12107
|
| |
Z3alpha |
Z3-alpha |
sat ✅
|
0.30178
|
0.20275
|
|
SMT-COMP 2025
|
0.17 (5/6) |
cvc5 |
cvc5 |
sat ✅
|
0.26605
|
0.14826
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.53334
|
0.68082
|
| |
SMT-RAT |
SMT-RAT |
sat ✅
|
0.36317
|
0.23860
|
| |
Yices2 |
Yices2 |
sat ✅
|
0.27126
|
0.15284
|
| |
Z3alpha |
Z3-alpha |
sat ✅
|
0.60287
|
0.49075
|
| |
Z3 |
Z3-alpha-base |
sat ✅
|
0.31731
|
0.19002
|
| |
|
z3siri-base |
sat ✅
|
0.30565
|
0.17721
|