Benchmark
non-incremental/QF_NRA/20240407-pPDA-Chiari-Pontiggia-Winkler/past/sqrt2by2_bern_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 a probabilistic pushdown automaton (pPDA) modelling a symmetric random walk on the non-negative integers. The walk is started at position 1 and flips a bit every time it moves towards 0. When it reaches 0, the bit is distributed according to a Bernoulli-sqrt(2)/2 distribution. However, 0 is only reached after infinitely many steps on average.
The SMT formula results from applying Theorem 8 from [1]. The SMT formula is SAT iff the automaton is PAST.
| Benchmark |
|---|
| Size | 2399 |
| Compressed Size | 909 |
| 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 | 2391 |
| Compressed Size | 913 |
| Max. Term Depth | 4 |
| Asserts | 12 |
| Declared Functions | 0 |
| Declared Constants | 6 |
| 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
|
0.40 (3/5) |
cvc5 |
cvc5 |
unsat ✅
|
0.60177
|
0.50205
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.42370
|
0.44013
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
12.03530
|
11.93560
|
| |
Yices2 |
Yices2 |
unknown ❌
|
1201.21636
|
1200.57622
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.32944
|
0.23000
|
|
SMT-COMP 2025
|
0.33 (4/6) |
cvc5 |
cvc5 |
unsat ✅
|
0.61014
|
0.49295
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.46745
|
0.45284
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.89990
|
0.78346
|
| |
Yices2 |
Yices2 |
unknown ❌
|
1201.25956
|
1200.97438
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.89337
|
1.71550
|
| |
Z3 |
Z3-alpha-base |
unsat ✅
|
0.56671
|
0.43695
|
| |
|
z3siri-base |
unsat ✅
|
0.45026
|
0.32838
|