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Dimensions in Synthesis Part 3: Ambiguity (Synthesis from Examples & Keywords)

Dimensions in Synthesis Part 3: Ambiguity (Synthesis from Examples & Keywords). Sumit Gulwani sumitg@microsoft.com Microsoft Research, Redmond. May 2012. Potential Users of Synthesis Technology. Algorithm Designers. Software Developers. Most Useful Target. End-Users.

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Dimensions in Synthesis Part 3: Ambiguity (Synthesis from Examples & Keywords)

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  1. Dimensions in Synthesis Part 3: Ambiguity (Synthesis from Examples & Keywords) Sumit Gulwani sumitg@microsoft.com Microsoft Research, Redmond May 2012

  2. Potential Users of Synthesis Technology Algorithm Designers Software Developers Most Useful Target End-Users Most Transformational Target Students and Teachers • Vision for End-users: Enable people to have (automated) personal assistants. • Vision for Education: Enable every student to have access to free & high-quality education.

  3. Intent Specification • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  4. Intent Specification ICSE 2010: SusmitJha, Gulwani, Seshia, Tiwari. • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  5. Synthesis from Logical Specification Turn off rightmost 1-bit Functional Specification: b Æ[(I[p]=1Æ (I[j]=0)) )(J[p]=0 Æ(J[j] = I[j]))] b j=p+1 jp p=1 Tool Output: J = I & (I-1) PLDI 2011: Gulwani, Jha, Tiwari, Venkatesan.

  6. Interactive Synthesis using Examples Turn-off rightmost contiguous string of 1’s User: I want a program that maps 01011 -> 01000 Tool: There exist at least two programs that match the spec Program 1: (x+1) & (x-1) Program 2: (x+1) & x But they differ on 00000 (Distinguishing Input) What should 00000 be mapped to? User: 00000 -> 00000  • 

  7. Interactive Synthesis using Examples Turn-off rightmost contiguous string of 1’s User: 01011 -> 01000 Tool: 00000 ? User: 00000 Tool: 01111 ? User: 00000 Tool: 00110 ? User: 00000 Tool: 01100 ? User: 00000 Tool: 01010 ? User: 01000 Tool: Your program is x & (1 + ((x-1)|x))

  8. Intent Specification • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  9. Intent Specification • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  10. Language for Constructing Output Strings Guarded Expression G := Switch((b1,e1), …, (bn,en)) String Expression e := Concatenate(f1, …, fn) Base Expression f := s // Constant String | SubStr(vi, p1, p2) Index Expression p := k // Constant Integer | Pos(r1, r2, k) // kth position in string whose left/right side matches with r1/r2 Notation: SubStr2(vi,r,k)´SubsStr(vi,Pos(²,r,k),Pos(r,²,k)) • Denotes kth occurrence of regular expression r in vi

  11. Example Format phone numbers Switch((b1, e1), (b2, e2)), where b1´Match(v1,NumTok,3), b2 ´:Match(v1,NumTok,3), e1´Concatenate(SubStr2(v1,NumTok,1), ConstStr(“-”), SubStr2(v1,NumTok,2), ConstStr(“-”), SubStr2(v1,NumTok,3)) e2´ Concatenate(ConstStr(“425-”),SubStr2(v1,NumTok,1), ConstStr(“-”),SubStr2(v1,NumTok,2))

  12. Key Synthesis Idea: Divide and Conquer Reduce the problem of synthesizing expressions into sub-problems of synthesizing sub-expressions. • Reduction requires computing all solutions for each of the sub-problems: • This also allows to rank various solutions and select the highest ranked solution at the top-level. • A challenge here is to efficiently represent, compute, and manipulate huge number of such solutions. • I will show three applications of this idea in the talk. • Read the paper for more tricks!

  13. Synthesizing Guarded Expression • Application #1: We reduce the problem of learning guarded expression P to the problem of learning string expressions for each input-output pair. Goal: Given input-output pairs: (i1,o1), (i2,o2), (i3,o3), (i4,o4), find P such that P(i1)=o1, P(i2)=o2, P(i3)=o3, P(i4)=o4. Algorithm: 1. Learn set S1 of string expressions s.t.8e inS1, [[e]] i1 = o1. Similarly compute S2, S3, S4. Let S = S1 ÅS2 ÅS3 ÅS4. 2(a) If S ≠ ; then result is Switch((true,S)).

  14. Example: Various choices for a String Expression Input Output Constant Constant Constant

  15. Synthesizing String Expressions Application #2: To represent/learn all string expressions, it suffices to represent/learn all base expressions for each substring of the output. Number of all possible string expressions (that can construct a given output string o1 from a given input string i1) is exponential in size of output string. • # of substrings is just quadratic in size of output string! • We use a DAG based data-structure, and it supports efficient intersection operation!

  16. Example: Various choices for a SubStr Expression Various ways to extract “706” from “425-706-7709”: • Chars after 1st hyphen and before 2nd hyphen. Substr(v1, Pos(HyphenTok,²,1), Pos(²,HyphenTok,2)) • Chars from 2nd number and up to 2nd number. Substr(v1, Pos(²,NumTok,2), Pos(NumTok,²,2)) • Chars from 2nd number and before 2nd hyphen. Substr(v1, Pos(²,NumTok,2), Pos(²,HyphenTok,2)) • Chars from 1st hyphen and up to 2nd number. Substr(v1, Pos(HyphenTok,²,1), Pos(²,HyphenTok,2)) 

  17. Synthesizing SubStr Expressions Application #3: To represent/learn all SubStr expressions, we can independently represent/learn all choices for each of the two index expressions. The number of SubStr(v,p1,p2) expressions that can extract a given substring w from a given string v can be large! • This allows for representing and computing O(n1*n2) choices for SubStr using size/time O(n1+n2).

  18. Back to Synthesizing Guarded Expression Goal: Given input-output pairs: (i1,o1), (i2,o2), (i3,o3), (i4,o4), find P such that P(i1)=o1, P(i2)=o2, P(i3)=o3, P(i4)=o4. Algorithm: Learn set S1 of string expressions s.t.8e inS1, [[e]] i1 = o1. Similarly compute S2, S3, S4. Let S = S1 ÅS2 ÅS3 ÅS4. 2(a). If S ≠ ; then result is Switch((true,S)). 2(b). Else find a smallest partition, say {S1,S2}, {S3,S4}, s.t.S1ÅS2 ≠ ; and S3ÅS4≠ ;. 3. Learn boolean formulas b1, b2s.t. b1 maps i1, i2 to true and i3, i4 to false. b2maps i3, i4to true and i1, i2to false. 4. Result is: Switch((b1,S1ÅS2), (b2,S3ÅS4))

  19. Ranking Strategy • Prefer shorter programs. • Fewer number of conditionals. • Shorter string expression, regular expressions. • Prefer programs with less number of constants.

  20. Intent Specification VLDB 2012/CAV 2012: Rishabh Singh, Gulwani • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  21. Intent Specification PLDI 2011: Bill Harris, Gulwani • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  22. Intent Specification CHI 2012: Salman Cheema, Gulwani, LaViola • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  23. Architecture (Partial) Sketch/Ink Strokes Sketch Recognition Engine [HCI] Circle/Line Objects Constraint Inference Engine [Machine Learning] Constraints between Objects Model Synthesis/Beautification Engine [Theorem Proving] (Partial) Drawing Pattern Synthesis Engine [Program Synthesis] Suggestions for Drawing Completion

  24. Intent Specification Joint work with: Vu Le, Zhendong Su (UC-Davis) • Examples • Bitvector Algorithms (ICSE ‘10) • Spreadsheet Macros (CACM ‘12) • Syntactic String Transformations (POPL ‘11) • Semantic String Transformations (VLDB ‘12) • Number Transformations (CAV ‘12) • Table Transformations (PLDI ‘11) • Sketch • Drawings (CHI 2012) • Keywords • SmartPhone Apps

  25. Potential Users of Synthesis Technology Algorithm Designers Software Developers Most Useful Target End-Users Most Transformational Target Students and Teachers • Vision for End-users: Enable people to have (automated) personal assistants. • Vision for Education: Enable every student to have access to free & high-quality education.

  26. Dimensions in Synthesis (Application) (Ambiguity) (Algorithm) • Concept Language • Programs • Straight-line programs • Automata • Queries • Sequences • User Intent • Logic, Natural Language • Examples, Demonstrations/Traces • Search Technique • SAT/SMT solvers (Formal Methods) • A*-style goal-directed search (AI) • Version space algebras (Machine Learning) PPDP 2010: “Dimensions in Program Synthesis”, Gulwani.

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