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IOF, ACSys and WMSO+U St ephane Demri CNRS Marie Curie Fellow - PowerPoint PPT Presentation

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IOF, ACSys and WMSO+U St ephane Demri CNRS Marie Curie Fellow Groupe de travail INFINI, January 2015 Overview 1 Marie Curie Fellowship IOF 2 ACSys Group Temporal Logics on Strings 3 2 Marie Curie Fellowship IOF 3 Marie Curie

  1. IOF, ACSys and WMSO+U St´ ephane Demri CNRS – Marie Curie Fellow Groupe de travail INFINI, January 2015

  2. Overview 1 Marie Curie Fellowship IOF 2 ACSys Group Temporal Logics on Strings 3 2

  3. Marie Curie Fellowship IOF 3 Marie Curie Fellowship IOF

  4. International Outgoing Fellowship (IOF) • Funding to carry out research abroad. • IOFs are for researchers from EU member states. • Minimal requirement: PhD. • Outgoing phasis (1 or 2 years) + return phasis (1 year). • Individual fellowships. 4 Marie Curie Fellowship IOF

  5. Non-flat (but flattable) system for Marie Curie fellowships Marie Curie Actions Research Fellowship Program is a EU initiative to promote research and innovation. IOF IEF EU EU IIF 5 Marie Curie Fellowship IOF

  6. Application form • Research program ( ≤ 8 pages) This includes presentation of host institutions. • Extended CV ( ≤ 7 pages). • Training objectives ( ≤ 2 pages). • Implementation ( ≤ 6 pages). • Impact ( ≤ 4 pages). • Deadline: so far early august (notification in december). Project can start up to 1 year after the final signature. • Acceptance rate: ∼ 15%. 6 Marie Curie Fellowship IOF

  7. ACSys Group 7 ACSys Group

  8. ACSys members • Analysis of Computer Systems group (ACSys) is part of Courant Institute of Mathematical Sciences (CIMS), New York University. • Faculty: Clark Barrett , Patrick Cousot, Ben Goldberg, Thomas Wies, Lenore Zuck. • Research fellow / visiting positions: Morgan Deters, Dejan Jovanovic, Eric Koskinen, Daniel Schwartz-Narbonne. • Ph.D. Students: Kshitij Bansal, Junjie Chen, Liana Hadarean, Tim King, Siddharth Krishna, Zvonimir Pavlinovic, Chanseok Oh, Wei Wang. 8 ACSys Group

  9. CVC4 group • CVC4: open-source automatic theorem prover for satisfiability modulo theories (SMT) problems. See Morgan’s slides or CVC4 web page. • Members at NYU: Clark Barrett , Morgan Deters, Kshitij Bansal, Liana Hadarean, Tim King. • Members at Iowa University and other places: Cesare Tinelli , Tianyi Liang, Andrew Reynolds, Dejan Jovanovic, Franc ¸ois Bobot, etc. • Leader among SMT solvers (performances, diversity of theories, participation to international standards such as SMT-LIB, etc.). 9 ACSys Group

  10. Other places in the area • Courant Institute of Mathematical Sciences (CIMS). • CUNY (S. Artemov, M. Fitting, R. Parikh). • Yale University (R. Piskac) • Columbia University • Princeton (New Jersey), MIT (Boston, Main), UPenn (Philadelphia, Pensylvania). 10 ACSys Group

  11. Overview of my research program there • Temporal logics modulo theories. See the second part of the talk. • Decision procedures for fragments of separation logic. 1 Two-variable fragment. [Demri & Deters, CSL-LICS’14] 2 One-variable fragment. [CSR’14] 3 Survey paper. [Demri & Deters, AIML ’14] • Verification of integer programs with SMT solvers. 1 Prototype: path schema enumeration. 2 Amit’s PhD thesis. 3 Survey paper. [Barrett & Demri & Deters, FROCOS’13] 11 ACSys Group

  12. Temporal Logics on Strings Joint work with Morgan Deters (New York University) See also recent LSV technical report online. 12 Temporal Logics on Strings

  13. Reasoning about strings • Need for string reasoning: program verification, analysis of web applications, etc. • Theory solvers for strings. [Liang et al. – Abdulla et al., CAV’14; Hutagalung & Lange, CSR’14] • Solving word equations. [Makanin, Math. 77; Plandowski, JACM 04] • What about reasoning on sequences of strings ? 13 Temporal Logics on Strings

  14. LTL on strings: LTL (Σ ∗ , � p ) • String variables SVAR = { x 1 , x 2 , . . . } . (x ∈ SVAR , w ∈ Σ ∗ ) • Terms: t ::= w | x | X x • Formulae: t � p t ′ | ¬ φ | φ ∧ φ | X φ | φ U φ ::= φ • Example: GF (( 001 � p x ) ∨ ( x � p 1001 )) ∧ G ( ¬ ( x � p X x )) 14 Temporal Logics on Strings

  15. A model with Σ = { 0 , 1 } x 1 000 011110 ε 1111 . . . x 2 101 010001 010001 00 . . . | = F ( x 2 � p X x 3 ) x 3 00 111 010001101 ε . . . 15 Temporal Logics on Strings

  16. The case Σ = { 0 } def = LTL (Σ ∗ , � p ) with Σ = { 0 } . • LTL ( N , ≤ ) • Satisfiability problem for LTL ( N , ≤ ) is PS PACE -complete. [Demri & D’Souza, IC 07; Demri & Gascon, TCS 08] See also [Segoufin & Torunczyk, STACS’11] • The PS PACE upper bound is preserved with several LTL extensions or with richer numerical constraints (but no successor relation). 16 Temporal Logics on Strings

  17. Logic LTL (Σ ∗ , clen ) • clen ( w , w ′ ) : length of the longest common prefix between w and w ′ in Σ ∗ . = clen ( t 0 , t ′ 0 ) ≤ clen ( t 1 , t ′ σ, i | 1 ) def ⇔ clen ([ t 0 ] i , [ t ′ 0 ] i ) ≤ clen ([ t 1 ] i , [ t ′ 1 ] i ) • Reduction from LTL (Σ ∗ , � p ) to LTL (Σ ∗ , clen ) . t � p t ′ �→ clen ( t , t ) ≤ clen ( t , t ′ ) . • In the sequel either Σ = [ 0 , k − 1 ] for some k ≥ 1 or Σ = N . 17 Temporal Logics on Strings

  18. Symbolic models for LTL ( N , ≤ ) . . . x 1 • • • • • = < < < = = < = < = < . . . x 2 • • • • • = = = = = = x 3 . . . • • • • • | = symb XX ( x 1 < X x 2 ) = = < < = = = = . . . • • • • • 1 < < < < < = = = = . . . • • • • • 0 + Local consistency between two consecutive positions. 18 Temporal Logics on Strings

  19. Rephrasing the satisfiability property φ is LTL ( N , ≤ ) satisfiable iff there is a symbolic model σ such that σ | = symb φ and σ has a concrete interpretation in N 19 Temporal Logics on Strings

  20. Characterisation for LTL ( N , ≤ ) • Usual notion of path π between two nodes. • Strict length of the path π : slen ( π ) = number of edges labelled by < . • Strict length between � x , i � and � x ′ , i ′ � : slen ( � x , i � , � x ′ , i ′ � ) = sup { slen ( π ) : path π from � x , i � to � x ′ , i ′ �} def • Symbolic model σ has a concrete interpretation iff any pair of nodes has a finite strict length. [Cerans, ICALP’94; Demri & D’Souza, IC 07] [Gascon, PhD thesis 07;Carapelle & Kartzow & Lohrey, CONCUR’13] 20 Temporal Logics on Strings

  21. When WMSO+U enters into the play • There are formulae φ in LTL ( N , ≤ ) for which the set of symbolic models satisfying φ symbolically and having a concrete interpretation is not ω -regular. [Demri & D’Souza, IC 07] def • σ | = U X φ ⇔ for every b ∈ N , there is a finite Y with card ( Y ) ≥ b such that σ | = φ ( Y ) . def = ¬ U X φ . B X φ [Boja´ ’04; Boja´ nczyk, CSL nczyk & Colcombet, LICS’06] • Symbolic models for LTL ( N , ≤ ) having a concrete interpretation can be characterized by a formula in Bool(MSO,WMSO+U). • This leads to decidability of CTL ⋆ ( N , ≤ ) . [Carapelle & Kartzow & Lohrey, CONCUR’13] (based on [Boja´ nczyk, STACS’12] ) nczyk & Toru´ 21 Temporal Logics on Strings

  22. Back to strings Simple but essential properties for clen ( · ) 0 0 0 1 0 2 w 1 0 0 0 0 w 2 → clen ( w 1 , w 2 ) ≤ len ( w 1 ) 0 0 0 1 0 2 w 0 0 0 0 0 1 3 5 6 w 1 0 0 0 2 1 4 w 2 . . . 0 0 0 3 1 3 w k → ∃ i , j ∈ [ 1 , k ] such that clen ( w 0 , w 1 ) < clen ( w i , w j ) (Pigeonhole Principle – card (Σ) = k ≥ 2) 0 0 0 1 0 2 0 0 0 0 1 3 5 w 0 0 0 0 0 1 3 5 and w 1 0 0 0 0 1 4 w 1 w 2 → clen ( w 0 , w 1 ) = clen ( w 0 , w 2 ) 22 Temporal Logics on Strings

  23. String compatible counter valuations • Counter valuation c : { clen ( t , t ′ ) : t , t ′ ∈ T } → N . • String-compatibility: � ( clen ( t , t ) ≥ clen ( t , t ′ )) t , t ′ ∈ T � � (( ( clen ( t 0 , t 1 ) < clen ( t i , t i ))) ∧ clen ( t 0 , t 1 ) = · · · = clen ( t 0 , t k )) t 0 ,..., t k ∈ T i ∈ [ 0 , k ] � ⇒ ( ( clen ( t 0 , t 1 ) < clen ( t i , t j ))) i � = j ∈ [ 1 , k ] � ( clen ( t , t ′ ) < clen ( t ′ , t ′′ )) ⇒ ( clen ( t , t ′ ) = clen ( t , t ′′ )) t , t ′ , t ′′ ∈ T • Size in O (( q + r ) k + 2 ) with card ( T ) = q + r . 23 Temporal Logics on Strings

  24. Characterisation • String compatibility is equivalent to the existence of a string valuation witnessing the values of the counters clen ( t , t ′ ) . • The exact statement is a bit more complex to be used after in the translation from LTL (Σ ∗ , clen ) to LTL ( N , ≤ ) . • Checking satisfiability of Boolean combinations of prefix constraints is NP-complete. (upper bound by reduction into QF Presburger arithmetic) • PS PACE can be obtained using word equations and Plandowski’s PS PACE upper bound. (suffix constraints can be added at no cost) 24 Temporal Logics on Strings

  25. Translation • Formula φ with constant strings w 1 , . . . , w q and, string variables x 1 , . . . , x r . def • For all i , j ∈ [ 1 , q ] , c i , j = clen ( w i , w j ) . def • T = { y 1 , . . . , y q } ∪ { x 1 , . . . , x r } ∪ { X x 1 , . . . , X x r } . • φ subst : replace each w i by y i . 1 • φ rig def = G ( � i , j ∈ [ 1 , q ] ( clen ( y i , y j ) = c i , j )) . 2 25 Temporal Logics on Strings

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