Precise bounds for presburger arithmetic and the reals with addition: Preliminary report

Berman, Leonard

doi:10.1109/sfcs.1977.23

Cited by 26 publications

(11 citation statements)

References 4 publications

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“…Similarly, Presburger constraints should be in a normal form since full Presburger logic has already a complexity higher than 2exptime, see e.g. [22,4]. It is worth observing that as far as memory resources are concerned, no exptime-complete problem is known to be solved in polynomial space.…”

Section: Our Motivationmentioning

confidence: 99%

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Complexity of modal logics with Presburger constraints

Demri¹,

Lugiez²

2010

Journal of Applied Logic

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We introduce the Extended Modal Logic EML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that EML satisfiability is only pspacecomplete by designing a Ladner-like algorithm. This extends a well-known and nontrivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we provide a logarithmic space reduction from a variant of Sheaves Logic SL into EML that allows us to establish that its satisfiability problem is also pspace-complete, significantly improving the best known upper bound.

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Section: Our Motivationmentioning

confidence: 99%

“…By the induction hypothesis, SAT(Y i , d + 1) returns true. Each passage to (guess-children-from-left-to-right) (4,5) as well as the passage to (final-checking) are successful steps because the numbers of children is computed from M . Consequently, SAT( X, d ) has an accepting computation.…”

Section: Case 1 ψ =mentioning

confidence: 99%

Complexity of modal logics with Presburger constraints

Demri¹,

Lugiez²

2010

Journal of Applied Logic

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“…Fischer and Rabin [20] proved lower bounds which were later refined [3,4,22] using alternation [11]. Upper bounds can be found in [19,32,42,50].…”

Section: Related Workmentioning

confidence: 99%

Proof Synthesis and Reflection for Linear Arithmetic

Chaieb

Nipkow

2008

J Autom Reasoning

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This article presents detailed implementations of quantifier elimination for both integer and real linear arithmetic for theorem provers. The underlying algorithms are those by Cooper (for Z ) and by Ferrante and Rackoff (for R). Both algorithms are realized in two entirely different ways: once in tactic style, i.e. by a proof-producing functional program, and once by reflection, i.e. by computations inside the logic rather than in the meta-language. Both formalizations are generic because they make only minimal assumptions w.r.t. the underlying logical system and theorem prover. An implementation in Isabelle/HOL shows that the reflective approach is between one and two orders of magnitude faster.

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“…As a direct consequence, a set that possesses a simple representation could unfortunately be represented in an unduly complicated way. Second, deciding if a given vector of integers is in a given set can be performed in linear time with ndd, while it is at least NP-hard [15,45] with Presburger formula and semi-linear sets.…”

Section: Number Decision Diagrams (Ndd)mentioning

confidence: 99%

FAST: acceleration from theory to practice

Bardin

Finkel

Leroux

et al. 2008

Int J Softw Tools Technol Transfer

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International audienceFast acceleration of symbolic transition systems (Fast) is a tool for the analysis of systems manipulating unbounded integer variables. We check safety properties by computing the reachability set of the system under study. Even if this reachability set is not necessarily recursive, we use innovative techniques, namely symbolic representation, acceleration and circuit selection, to increase convergence. Fast has proved to perform very well on case studies. This paper describes the tool, from the underlying theory to the architecture choices. Finally, Fast capabilities are compared with those of other tools. A range of case studies from the literature is investigated

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Precise bounds for presburger arithmetic and the reals with addition: Preliminary report

Cited by 26 publications

References 4 publications

Complexity of modal logics with Presburger constraints

Complexity of modal logics with Presburger constraints

Proof Synthesis and Reflection for Linear Arithmetic

FAST: acceleration from theory to practice

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