Hi, Following the attached thread from December 2020. When working with version 2.9.4 of Spot, I got an endless runtime when I tried to create a small BA of this formula: (!(G({(a)} |=> {(b)[*32]}))) Thanks to your help, I understood that there was a bug in the mechanism that should avoid the WDBA-minimization in cases it creates to much additional states. (alexandre opened an issue for me – https://gitlab.lrde.epita.fr/spot/spot/-/issues/443) Was this bug fixed in any of the later versions? I met some additional problematic formulas. Currently, my only option to process such formulas is to avoid the WDBA-minimization step. Thanks in advance, Roei ******************* -----Original Message----- From: Roei Nahum Sent: Tuesday, December 8, 2020 5:40 PM To: Alexandre Duret-Lutz &lt;adl(a)lrde.epita.fr&gt; Subject: RE: [Spot] Spot question Great, now I get it. Thanks for the clarifications and debugging. I appreciate the time you spent to help. Roei ******************* -----Original Message----- From: Alexandre Duret-Lutz &lt;adl(a)lrde.epita.fr&gt; Sent: Tuesday, December 8, 2020 3:13 PM To: Roei Nahum &lt;roeina(a)nvidia.com&gt; Subject: Re: [Spot] Spot question External email: Use caution opening links or attachments On Tue, Dec 8, 2020 at 12:32 PM Roei Nahum &lt;roeina(a)nvidia.com&gt; wrote: A subset of LTL formulas, representing what are known as "obligation properties", can be translated into Weak Deterministic Büchi Automata. Those WDBA can be minimized using techniques similar to DFA minimization, i.e. in O(n log n), while minimization of DBA in general is NP-complete. So whenever you translate an LTL formula with an optimization level set to High (the default), and even if you do not specifically asked for a deterministic automaton, the translator will try to determinize your automaton and check if it is a WDBA to minimize it. Quite often, the minimal WDBA obtained is smaller than the non-deterministic BA that we were able to construct otherwise. See https://nam11.safelinks.protection.outlook.com/?url=https:%2F%2Fwww.lrde.ep… for a high-level view of the LTL translation pipeline. And references to the WDBA papers. Using "!wdba-minimize" is simply disabling the bottom branch, but you still get some simulation-based reductions in the top branch. A quite dated benchmark from around the time when WDBA minimization was introduced in Spot shows the effect of activating it: https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.lrde.… (The option names at the bottom of the first page are unrelated to those used today.) I consider this option to be the most useful automaton simplification in Spot, and the reason why automata produced by Spot are often smaller than those of other tools. (Hence the reason why I called this the "secret weapon" of Spot in the aforementioned slides.) The main problem with WDBA is that it requires a determinization. In the case of !G({a} |=> {b[*32]}), which can also be written as F(a & F[1:32]!b), there is a non-deterministic choice on the first state (see attachment). The determinization (a simple powerset construction) creates an exponential number of states, before the minimization has a chance to reduce it to 34 states. In fact for this particular kind of automata (with a "terminal" accepting state), I believe I should be able to write a smarter determinization that would keep 34 states in this very case. The 2.9.x versions are just bug fixes above version 2.9 released in April. The latest is 2.9.5, but if 2.9.4 works for you, there is no serious reason to upgrade. On the development version of Spot, which will probably be released as 2.10 early next year, I have made some changes meant to abort some determinization-based algorithms when they are optional and take too long. In the case of WDBA-minimization, the determinization is now meant to be aborted whenever it would create more than 4096 additional states. But you just highlighted a bug in that implementation. With the fix, I now see this: % for i in $(seq 1 32); do ./ltl2tgba "F(a & F[1:$i]\!b)" --stats="i=$i: %s states, %rs, det=%d"; done i=1: 3 states, 0.00108319s, det=1 i=2: 4 states, 0.00154409s, det=1 i=3: 5 states, 0.00198193s, det=1 i=4: 6 states, 0.00286866s, det=1 i=5: 7 states, 0.00366207s, det=1 i=6: 8 states, 0.00516698s, det=1 i=7: 9 states, 0.00783739s, det=1 i=8: 10 states, 0.0136073s, det=1 i=9: 11 states, 0.0108086s, det=0 i=10: 12 states, 0.0147442s, det=0 i=11: 13 states, 0.0231776s, det=0 i=12: 14 states, 0.0161911s, det=0 i=13: 15 states, 0.0161992s, det=0 i=14: 16 states, 0.0164307s, det=0 i=15: 17 states, 0.017823s, det=0 i=16: 18 states, 0.0197592s, det=0 i=17: 19 states, 0.0197573s, det=0 i=18: 20 states, 0.0203755s, det=0 i=19: 21 states, 0.020358s, det=0 i=20: 22 states, 0.0218632s, det=0 i=21: 23 states, 0.0229568s, det=0 i=22: 24 states, 0.0234896s, det=0 i=23: 25 states, 0.0295049s, det=0 i=24: 26 states, 0.0254808s, det=0 i=25: 27 states, 0.0256344s, det=0 i=26: 28 states, 0.0266605s, det=0 i=27: 29 states, 0.028628s, det=0 i=28: 30 states, 0.0296059s, det=0 i=29: 31 states, 0.0304871s, det=0 i=30: 32 states, 0.0319202s, det=0 i=31: 33 states, 0.0332124s, det=0 i=32: 34 states, 0.0340735s, det=0 See how the translation stopped building deterministic automata at i=9. Without WDBA-minimization you'd get non-deterministic automata everywhere. If my plan for a better determinization for terminal automata works I hope to get deterministic automata on all those lines. -- Alexandre Duret-Lutz External email: Use caution opening links or attachments ******************* On Tue, Dec 8, 2020 at 8:07 AM Roei Nahum &lt;roeina(a)nvidia.com&gt; wrote: Humm, this formula seems to be taking an exponential time to translate: % for i in $(seq 1 20); do ltl2tgba --small -B -f "(!(G({(a)} |=> {(b)[*$i]})))" --stats="i=$i: %s states, %rs"; done i=1: 3 states, 0.000980134s i=2: 4 states, 0.00161671s i=3: 5 states, 0.00199145s i=4: 6 states, 0.00283387s i=5: 7 states, 0.00336581s i=6: 8 states, 0.00495071s i=7: 9 states, 0.00683196s i=8: 10 states, 0.0120013s i=9: 11 states, 0.00975352s i=10: 12 states, 0.0136751s i=11: 13 states, 0.0231716s i=12: 14 states, 0.0372669s i=13: 15 states, 0.0729032s i=14: 16 states, 0.153856s i=15: 17 states, 0.299823s i=16: 18 states, 0.656352s i=17: 19 states, 1.48609s i=18: 20 states, 3.0405s i=19: 21 states, 6.51409s i=20: 22 states, 13.3897s Passing --low (that's "trans.set_level(spot::postprocessor::Low);" for you) to remove all simplifications seems to produce automata of equivalent size much faster: % for i in $(seq 16 32); do ltl2tgba --small -B --low -f "(!(G({(a)} |=> {(b)[*$i]})))" --stats="i=$i: %s states, %rs"; done i=16: 18 states, 0.0013444s i=17: 19 states, 0.00170704s i=18: 20 states, 0.00172487s i=19: 21 states, 0.00159999s i=20: 22 states, 0.00181502s i=21: 23 states, 0.00237525s i=22: 24 states, 0.00208415s i=23: 25 states, 0.00253886s i=24: 26 states, 0.00216258s i=25: 27 states, 0.00239979s i=26: 28 states, 0.00271767s i=27: 29 states, 0.0025924s i=28: 30 states, 0.00297612s i=29: 31 states, 0.00285316s i=30: 32 states, 0.00323873s i=31: 33 states, 0.00352748s i=32: 34 states, 0.00316449s Alternatively, it's possible to keep all simplifications on, but just disable WDBA-minimization with % ltl2tgba --small -B -x '!wdba-minimize' -f "(!(G({(a)} |=> {(b)[*32]})))" --stats="%s states, %rs" 34 states, 0.0236776s To do the above in C++, you need to create and option_map object and pass it to the translator object, as in : ... spot::option_map extra_options; extra_options.set("wdba-minimize", 0); spot::bdd_dict_ptr dict = spot::make_bdd_dict(); spot::translator trans(dict, &extra_options); ... I'll look more into it, because I thought I had fixed that problem in the development version of Spot a couple of months ago, but I can still reproduce it. I'll post updates on https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.lr… -- Alexandre Duret-Lutz ******************* HI, My name is Roei Nahum. I recently got to know SPOT, and first of all, I want to thank you for this great platform. I’m having an issue and I’ll appreciate if you can assist. I use SPOT in order to translate temporal formulas into automata. To do so, I downloaded spot, and wrote a C++ program based on SPOT API. The program I wrote is basically like this: …get the formula… spot::parsed_formula cex_pf = spot::parse_infix_psl(formula); if(cex_pf.format_errors(std::cerr)){ cout << "Invalid formula syntax: " << formula << endl; exit(1) } spot::translator trans; trans.set_type(spot::postprocessor::BA); trans.set_pref(spot::postprocessor::Small); twa_graph_ptr aut = trans.run(cex_pf.f); …print the automata… I tried running this code on several formulas, and it works great. The problems started when I processed this formula: G({(a)} |=> {(b)[*32]}) The code is running for a long time (more than a hour) without giving a result. Did it get stuck? Is there any way I can make it work? Thanks, Roei Nahum