Return-Path: Delivered-To: fp+@ux8.sp.cs.cmu.edu Received: from CS.CMU.EDU ([128.2.222.173]) by ux8.sp.cs.cmu.edu id aa25841; 30 Apr 2004 0:13 EDT Received: from web41902.mail.yahoo.com ([66.218.93.153]) by cs.cmu.edu id aa17505; 30 Apr 2004 0:12 EDT Message-ID: <20040430041221.47031.qmail@web41902.mail.yahoo.com> Received: from [151.201.246.142] by web41902.mail.yahoo.com via HTTP; Thu, 29 Apr 2004 21:12:21 PDT Date: Thu, 29 Apr 2004 21:12:21 -0700 (PDT) From: Donald Smith Subject: Progress Report To: Frank Pfenning In-Reply-To: <27690.1082596875@altosax.concert.cs.cmu.edu> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="0-188549619-1083298341=:46770" X-UIDL: d506cec4dfe29fc87eb7f8e1f48afcf6 --0-188549619-1083298341=:46770 Content-Type: text/plain; charset=us-ascii April 29: Progress Report/Plan I found two formulas ('30b' and 31) which are provable quickly using focussing alone but which are unprovable using focussing+Dyckhoff's technique (even with the maximum depth of iterative deepening set to a high value -- it reaches the maximum depth quickly). I don't know if this is because of a bug in my code, or if Dyckhoff's method is inherently incomplete when combined with focussing. If I copy assumptions (exists(_,_)=>B) into SynchronousLeft, Dyckhoff's method succeeds on one of the examples ('30b'). Even if it turns out that Dyckhoff's method IS incomplete, it is still faster on most theorems (significantly faster on some). So if a formula is unprovable with Dykhoff's method, the theorem prover could try with focussing alone. I combined prover.pl and proverD.pl into a single, new module prover.pl. The user can choose between using and not using Dyckhoff by the predicates d/0 and d/1. I wrote a procedure in Scheme to convert Gandalf examples to Prolog syntax. I also wrote a procedure in Prolog to convert Prolog examples to Gandalf syntax. I've been comparing Gandalf with my prover(s). Generally, Gandalf is much faster (often orders of magnitude faster). There are formulas that Gandalf solves quickly but my prover couldn't solve in an hour. But there are some examples on which my prover is faster (e.g., 7.3 seconds for Gandalf, <1 mls for mine; 47 mls for Gandalf, <1 mls for mine). Disturbingly, I found formulas (sics1.6 and sics1.6-2) listed among Gandalf's examples for which Gandalf terminates saying that they are not theorems, but my prover proved them immediately (in less than 1 mls). There are also formulas that cause Gandalf to crash, and there are formulas that cause SWI-Prolog (or gprolog) to crash (and it's not from stack overflow, apparently -- I think it's from a bug in SWI-Prolog). (cygwin is convenient.) -------------------------- Plan: Try to figure out why my implementation of focussing+Dyckoff is incomplete on those two examples. Continue benchmarking. Try to draw conclusions from the benchmark results. See if I can determine whether Gandalf is incomplete (it returns #f on some examples for which my prover finds a proof). For those examples which Gandalf solves quickly but which my prover takes too long to wait, try to determine whether they're really theorems or whether they're provable in sufficient time (e.g., overnight). Don --------------------------------- Do you Yahoo!? Win a $20,000 Career Makeover at Yahoo! HotJobs --0-188549619-1083298341=:46770 Content-Type: text/html; charset=us-ascii

April 29: Progress Report/Plan

I found two formulas ('30b' and 31) which are provable quickly using focussing alone but which are unprovable using focussing+Dyckhoff's technique (even with the maximum depth of iterative deepening set to a high value -- it reaches the maximum depth quickly). I don't know if this is because of a bug in my code, or if Dyckhoff's method is inherently incomplete when combined with focussing. If I copy assumptions (exists(_,_)=>B) into SynchronousLeft, Dyckhoff's method succeeds on one of the examples ('30b').

Even if it turns out that Dyckhoff's method IS incomplete, it is still faster on most theorems (significantly faster on some). So if a formula is unprovable with Dykhoff's method, the theorem prover could try with focussing alone.

I combined prover.pl and proverD.pl into a single, new module prover.pl. The user can choose between using and not using Dyckhoff by the predicates d/0 and d/1.

I wrote a procedure in Scheme to convert Gandalf examples to Prolog syntax.

I also wrote a procedure in Prolog to convert Prolog examples to Gandalf syntax.

I've been comparing Gandalf with my prover(s). Generally, Gandalf is much faster (often orders of magnitude faster). There are formulas that Gandalf solves quickly but my prover couldn't solve in an hour. But there are some examples on which my prover is faster (e.g., 7.3 seconds for Gandalf, <1 mls for mine; 47 mls for Gandalf, <1 mls for mine).

Disturbingly, I found formulas (sics1.6 and sics1.6-2) listed among Gandalf's examples for which Gandalf terminates saying that they are not theorems, but my prover proved them immediately (in less than 1 mls). There are also formulas that cause Gandalf to crash, and there are formulas that cause SWI-Prolog (or gprolog) to crash (and it's not from stack overflow, apparently -- I think it's from a bug in SWI-Prolog).

(cygwin is convenient.)
--------------------------
Plan:

Try to figure out why my implementation of focussing+Dyckoff is incomplete on those two examples.

Continue benchmarking.

Try to draw conclusions from the benchmark results.

See if I can determine whether Gandalf is incomplete (it returns #f on some examples for which my prover finds a proof).

For those examples which Gandalf solves quickly but which my prover takes too long to wait, try to determine whether they're really theorems or whether they're provable in sufficient time (e.g., overnight).

Don

Do you Yahoo!?
Win a $20,000 Career Makeover at Yahoo! HotJobs --0-188549619-1083298341=:46770--