Intelligence Artificial Intelligence Ian Gent More IJCAI 99

Intelligence Artificial Intelligence Part I :SAT for Data Encryption Part II: Automated Discovery in Maths Part III: Expert level Bridge player Three more papers from IJCAI

3 SAT for data encryption z“Using Walk-SAT and Rel-SAT for cryptographic key search” zFabio Massacci, Univ. di Roma I “La Sapienza” zProceedings IJCAI 99, pages zChallenge papers section yRel-SAT? A variant of Davis-Putnam with added “CBJ” yWalk-SAT? A successful incomplete SAT algorithm

4 Cryptography background zPlaintext P, Cyphertext C, Key K z(can encode each as sequence of bits) zCryptographic algorithm is function E yC = E K (P) zIf you don’t know K, it is meant to be hard to calculate yP = E K -1 (C)

5 Data Encryption Standard zMost widely used encryption standard by banks zPredates more famous “public key” cryptography zDES encodes blocks of 64 bits at a time zKey is length 56 bits zLoop 16 times ybreak the plaintext in 2 ycombine one half with the key using “clever function” f yXOR combination with the other half yswap the two parts zSecurity depends on the 16 iterations and on f

6 Aim of Paper zAnswer question “Can we encode cryptographic key search as a SAT problem so that AI search techniques can solve it?” zProvide benchmarks for SAT research yhelp to find out which algorithms are best yfailures and successes help to design new algorithms zDon’t expect to solve full DES yextensive research by special purpose methods yaim to study use of general purpose methods

7 DES as a SAT problem zUse encoding of DES into SAT zEach bit of C, P, K, is propositional variable zOperation of f is transformed into boolean form yCAD tools used separately to optimise this zFormulae corresponding to each step of DES zThis would be huge and unwieldy, so y“clever optimisations” inc. some operations precomputed zResult is a SAT formula  (P,K,C) yremember bits are variable, so this encodes the algorithm xnot a specific plain text zset some bits (e.g. bits of C) for specific problem

8 Results zWe can generate random keys, plaintext yunlimited supply of benchmark problems yproblems should be hard, so good for testing algorithms zResults yWalk-SAT can solve 2 rounds of DES yRel-SAT can solve 3 rounds of DES ycompare specialist methods, solving up to 12 rounds zHave not shown SAT can effectively solve DES zShown an application of SAT,and new challenges

9 Automated Discovery in Maths z“Automatic Concept Formation in Pure Mathematics” zSimon Colton, Alan Bundy yUniversity of Edinburgh zToby Walsh yUniversity of Strathclyde (now York) zProceedings of IJCAI-99, pages yMachine Learning Section zIntroduces the system HR ynamed for Hardy & Ramunajan, famous mathematicians zDiscovered novel mathematical concepts

10 Concept Formation zHR uses a data table for concepts zA concept is a rule satisfied by all entries in the table zStart with some initial concepts ye.g. axioms of group theory yuse logical representation of rules, I.e. “predicates” zNow we need to do two things yproduce new concepts yidentify some of the new ones as interesting xto avoid exponential explosion of dull concepts

11 Production rules zUse 8 production rules to generate new concepts ynew table, and definition of new predicate ye.g. “match” production rule xfinds rows where columns are equals xe.g. in group theory, general group A*B = C xmatch rule gives new concept “A*A = A” zProduction rules can combine two old concepts zClaim that these 8 can produce interesting concepts zNo claim that all interesting concepts covered

12 Heuristic Score of Concepts zWant to identify promising concepts zParsimony ylarger data tables are less parsimonious zComplexity yfew production rules necessary means less complex zNovelty ynovel concepts don’t already exist zConcepts and production rules can be scored ypromising ones used

13 Results zCan use HR to build mathematical theories zThis paper uses group theory zHR has introduced novel concepts into the handbook of integer sequences ze.g. Refactorable numbers ythe number of factors of a number is itself a factor ye.g. 9 is refactorable xthe 3 factors are 1, 3, 9. So 9 is refactorable

14 Expert level bridge play z“GIB: Steps towards an expert level bridge playing program” zMatthew Ginsberg, Oregon University zProceedings IJCAI 99, pages zComputer Game Playing section

15 Expert level bridge play zAren’t games well attacked by AI? yDeep Blue, beat Kasparov yChinook, World Man-Machine checkers champion xsubject of a later lecture yConnect 4 solved by computer zLittle progress on on 19x19 board x because of two types of game yGo, Oriental game huge branching rate yCard games like bridge xbecause of uncertain information, I.e. other players cards

16 What’s the problem? zIf we knew location of all cards, no problem y<< 52! Sequences of play, because of suit following ydramatically less than games like chess xone estimate is zWe have imperfect information yestimates of quality of play have to be probabilistic zTo date, computer bridge playing very weak ySlightly below average club player y“They would have to improve to be hopeless” xBob Hamman, six time winner of Bermuda Bowl

17 What’s the solution? zGinsberg implemented brilliantly simple idea zPretend we do know the location of cards yby dealing them out at random zFind best play with this known position of cards yscore initial move by expected score of hand zRepeat a number of times (e.g. 50, 100) zPick out move which has best average score zThis is called the “Monte Carlo” method ystandard name in many areas where random data is generated to simulate real data

18 GIB zGinsberg implemented (and sells) system called GIB zBest play in given deal found by standard methods ygeneral methods subject of forthcoming lectures zDealt at random consistent with existing knowledge ycards played to date, bidding history zSeparate method for bidding (less successful) zGIB has some good results ywon every match in 1998 World Computer Championship ylost to Zia Mahmoud & Michael Rosenberg by 6.4 IMPs xsurprisingly close, though only over short match