Succinct Representation, Leaf Languages, and Projection Reductions

Veith, Helmut

doi:10.1006/inco.1997.2696

Cited by 30 publications

(17 citation statements)

References 20 publications

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“…For example, the problem of deciding EF p (reachability) is complete for nondeterministic logspace-NL, while in BDD representation it becomes complete for PSPACE. Similar results can be shown for other Boolean formalisms and are closely tied to principal questions in structural complexity theory [Gottlob et al 1999;Veith 1997Veith , 1998b]. …”

Section: Path Quantifiers: Asupporting

confidence: 76%

Counterexample-guided abstraction refinement for symbolic model checking

Clarke

Grumberg

Jha

et al. 2003

J. ACM

Self Cite

755

585

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Abstract. We present an automatic iterative abstraction-refinement methodology in which the initial abstract model is generated by an automatic analysis of the control structures in the program to be verified. Abstract models may admit erroneous (or "spurious") counterexamples. We devise new symbolic techniques which analyze such counterexamples and refine the abstract model correspondingly. The refinement algorithm keeps the size of the abstract state space small due to the use of abstraction functions which distinguish many degrees of abstraction for each program variable. We describe an implementation of our methodology in NuSMV. Practical experiments including a large Fujitsu IP core design with about 500 latches and 10000 lines of SMV code confirm the effectiveness of our approach.

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Section: Path Quantifiers: Asupporting

confidence: 76%

Counterexample-guided abstraction refinement for symbolic model checking

Clarke

Grumberg

Jha

et al. 2003

J. ACM

Self Cite

755

585

View full text Add to dashboard Cite

show abstract

“…In fact, it holds under the requirement that the logspace reduction is also a polylogtime reduction (PLT). Briefly, a map f : → from a problem to a problem is a PLT-reduction, if there are polylogtime deterministic Turing machines N and M such that for all w, N (w) = | f (w)| and for all w and n, M (w, n) = Bit(n, f (w)), that is, the nth bit of f (w) (see e.g., Veith [1998] for details). (Recall that N and M have separate input tapes whose cells can be accessed by use of an index register tape.)…”

Section: Proofmentioning

confidence: 99%

“…The strongest form of the conversion lemma appears in Veith [1998], where X is PLT and Y is monotone projection reducibility [Immerman 1987]. Informally, monotone projection reductions are reductions that transform a relational data structure A into a relational data structure B such that each tuple in B is the projection of a single tuple in A.…”

Section: Hardnessmentioning

confidence: 99%

“…The conversion lemma gives rise to an upgrading theorem, which has been subsequently sharpened [Balcázar et al 1992;Eiter et al 1994;Gottlob et al 1995;Veith 1998] and is stated below in the strongest form of Veith [1998]. For a complexity class C, denote long(C) = {long(L) | L ∈ C}, where long(L) = bin(n)∈1L {0, 1} n , that is, contains all strings of length n such that n, in binary and with the leading 1 omitted, belongs to L.…”

Section: Hardnessmentioning

confidence: 99%

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Complexity and expressive power of logic programming

et al. 2001

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This article surveys various complexity and expressiveness results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming.

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“…They also provided sufficiency conditions for problems that become intractable when inputs are represented in this way. Veith [Vei95,Vei96] showed that, even when inputs are represented using Boolean formulae (instead of circuits), a problem's computational complexity can experience an exponential blowup. He also gave sufficiency conditions for when the problems become hard.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Feigenbaum¹,

Kannan²,

Vardi³

et al. 1999

Chicago J. of Theoretical Comp. Sci.

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To analyze the complexity of decision problems on graphs, one normally assumes that the input size is polynomial in the number of vertices. Galperin and Wigderson [GW83] and, later, Papadimitriou and Yannakakis [PY86] investigated the complexity of these problems when the input graph is represented by a polylogarithmically succinct circuit. They showed that, under such a representation, certain trivial problems become intractable and that, in general, there is an exponential blowup in problem complexity. Later, Balcázar, Lozano, and Torán [Bal96, BL89, BLT92, Tor88] extended these results to problems whose inputs are structures other than graphs. In this paper, we show that, when the input graph is represented by an ordered binary decision diagram (OBDD), there is an exponential blowup in the complexity of most graph problems. In particular, we show that the GAP and AGAP problems become complete for PSPACE and EXP, respectively, when the graphs are succinctly represented by OBDDs.

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Succinct Representation, Leaf Languages, and Projection Reductions

Cited by 30 publications

References 20 publications

Counterexample-guided abstraction refinement for symbolic model checking

Counterexample-guided abstraction refinement for symbolic model checking

Complexity and expressive power of logic programming

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