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Widening ROBDDs with Prime Implicants [chapter]

Neil Kettle, Andy King, Tadeusz Strzemecki
2006 Lecture Notes in Computer Science  
This paper proposes a widening that can be used to both constrain the size of an ROBDD and also ensure that the number of times that it is weakened is bounded by some given constant.  ...  The widening can be used to either systematically approximate from above (i.e. derive a weaker function) or below (i.e. infer a stronger function).  ...  The formula ¬(x ↔ y) = (x ∧ ¬y) ∨ (¬x ∧ y) is actually a quadratic prime implicant and this hints at an ROBDD widening.  ... 
doi:10.1007/11691372_7 fatcat:ijsr4atas5gwln4733t5admej4

Two classes of Boolean functions for dependency analysis

Tania Armstrong, Kim Marriott, Peter Schachte, Harald Søndergaard
1998 Science of Computer Programming  
On the practical side, we investigate various representations for the classes based on reduced ordered binary decision diagrams (ROBDDs), disjunctive normal form, conjunctive normal form, Blake canonical  ...  More precisely, an implicant of F is a term that implies F. An implicant is prime if no proper subterm is an implicant.  ...  For larger tests it is several times faster than ROBDDs, and the performance gap widens with larger tests, suggesting that DBCFD~ would scale better to large programs.  ... 
doi:10.1016/s0167-6423(96)00039-1 fatcat:myvly7jm7bbytb57zurobdmz4y

Approximate Quantifier Elimination for Propositional Boolean Formulae [chapter]

Jörg Brauer, Andy King
2011 Lecture Notes in Computer Science  
The method is based on computing prime implicants using SAT and successively refining overapproximations of a given formula.  ...  This contrasts with classical monolithic (all or nothing) approaches based on resolution or model enumeration.  ...  Acknowledgment We thank Olivier Coudert for discussions on the complexity of finding the smallest prime implicant.  ... 
doi:10.1007/978-3-642-20398-5_7 fatcat:rk5p34jcmvgcbneoyzxzbgmnu4

Existential Quantification as Incremental SAT [chapter]

Jörg Brauer, Andy King, Jael Kriener
2011 Lecture Notes in Computer Science  
The algorithm combines model enumeration with the generation of shortest prime implicants so as to converge onto a quantifier-free formula presented in CNF.  ...  This approach contrasts with existing techniques in that it is based solely on manipulating the SAT instance rather than requiring any reengineering of the SAT solver or needing an auxiliary data-structure  ...  Methods based on primes and cubes Prime implicants have been directly applied to widening Boolean functions represented as ROBDDs [24] .  ... 
doi:10.1007/978-3-642-22110-1_17 fatcat:cuvr7mvz3faore346ooffap3cm

Combining predicate and numeric abstraction for software model checking

Arie Gurfinkel, Sagar Chaki
2010 International Journal on Software Tools for Technology Transfer (STTT)  
All our data structures combine BDDs (for efficient propositional reasoning) with data structures for representing numerical constraints.  ...  Furthermore, the domain is extended implicitly with "primed" propositional variables V ′ P {p ′ | p ∈ V P } . The meaning of each predicate p in V P is given by the concretization function γ.  ...  Binary Decision Diagrams Reduced Ordered Binary Decision Diagrams (ROBDDs, or BDDs for the purpose of this paper) [7] are a canonical representation of propositional formulas.  ... 
doi:10.1007/s10009-010-0162-x fatcat:a2dfruavqjfebdegernedypycm

Combining Predicate and Numeric Abstraction for Software Model Checking

Arie Gurfinkel, Sagar Chaki
2008 2008 Formal Methods in Computer-Aided Design  
All our data structures combine BDDs (for efficient propositional reasoning) with data structures for representing numerical constraints.  ...  Furthermore, the domain is extended implicitly with "primed" propositional variables V ′ P {p ′ | p ∈ V P } . The meaning of each predicate p in V P is given by the concretization function γ.  ...  Binary Decision Diagrams Reduced Ordered Binary Decision Diagrams (ROBDDs, or BDDs for the purpose of this paper) [7] are a canonical representation of propositional formulas.  ... 
doi:10.1109/fmcad.2008.ecp.21 dblp:conf/fmcad/GurfinkelC08 fatcat:2ksd5xgin5estp5ugfvgwddqhu

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Julian F. Miller, Dominic Job, Vesselin K. Vassilev
2012 Genetic Programming and Evolvable Machines  
A prime implicant is called essential when it implies at least one minterm that is not implied by any other prime implicant of the function.  ...  A prime implicant is a product term that cannot be combined with any other product term to generate a term with fewer literals than the original term.  ... 
doi:10.1023/a:1010016313373 fatcat:iznfnit4jva6rpnhtkefqfh2xq

Effective and efficient circuit synthesis for LUT FPGAs:based on functional decomposition and information relationship measures [article]

Chojnacki, A (Artur), Stevens, MPJ (Mario), Otten, RHJM (Ralph), Jozwiak, L (Lech)
2004
In the proposed method, all crucial decisions are made with the use of the theory of information relationships and information relationship measures [Jóź97a] during the decomposition process.  ...  Smallest implicant divisor -The smallest implicant, i.e., implicant with fewest literals, is detected as the shortest path in ROBDD from the root node to any leaf nodes.  ...  . , s n ) with s i ∈ S i , and we write S = S 1 ⊗ S 2 ⊗ · · · ⊗ S n = ⊗ 1≤i≤n S i = {(s 1 , . . . , s n )|s i ∈ S i }. (1, prime); (2, even); (2, odd); (2, prime); (3, even); (3, odd); (3, prime); (4,  ... 
doi:10.6100/ir582596 fatcat:7qhyp5av6vguhjuxsstvijbxh4

Formal Verification of Object-Oriented Software. Papers presented at the 2nd International Conference, October 5-7, 2011, Turin, Italy

Bernhard [Hrsg.] Beckert, Ferruccio [Hrsg.] Damiani, Dilian [Hrsg.] Gurov
2011
Then, we weaken the premiss of the implication on the right, replacing U m.a m .e with U m.a m.e.  ...  ) and low (robdd-refs) level: robdd t1 =⇒ robdd t2 =⇒ interp t1 = interp t2 =⇒ struct-equal t1 t2 robdd-refs t1 =⇒ robdd-refs t2 =⇒ interp t1 = interp t2 =⇒ struct-equal t1 t2 Moreover we can show that  ...  A variable V is evaluated over I(0), whereas its primed resp. double primed version V ′ resp. V ′′ is evaluated over I ′ (0) and I(1) respectively.  ... 
doi:10.5445/ir/1000024780 fatcat:qnqnk6c46jcrxjgydp6migtxpm