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Topic: Presburger arithmetic

Related Topics

Peano axioms

Predicate calculus

Entscheidungsproblem

On Computable Numbers

Ta Kung Pao

1929 in science

Exotic option

George Town, Penang

Cathedral of Saint John the Divine

1929

University of Georgia

	Presburger arithmetic - Wikipedia, the free encyclopedia
		Presburger arithmetic is the first-order theory of the natural numbers with addition.
		Again, such a proof cannot be given for general arithmetic; in fact, it follows from Gödel's incompleteness theorem that (any recursive axiomatization of) general arithmetic cannot be both consistent and complete.
		Presburger arithmetic is an interesting example in computational complexity theory and computation because Fischer and Rabin proved in 1974 that every algorithm which decides the truth of Presburger statements has a worst-case runtime of at least
	en.wikipedia.org /wiki/Presburger_arithmetic (701 words)

	Presburger arithmetic
		Presburger[?] proved in 1929 that there is an algorithm which decides for any given statement in Presburger arithmetic whether it is true or not.
		Again, this is false for general arithmetic; this is the content of Gödel's incompleteness theorem.
		Presburger arithmetic is an interesting example in computational complexity theory and computation because Fischer and Rabin proved in 1974 that every algorithm which decides the truth of Presburger statements has a runtime of at least 2^(2^(cn)) for some constant c.
	ebroadcast.com.au /lookup/encyclopedia/pr/Presburger_arithmetic.html (415 words)

	PlanetMath: Presburger arithmetic
		Presburger arithmetic is a weakened form of arithmetic which includes the structure
		Presburger arithmetic is decideable, but is consequently very limited in what it can express.
		This is version 3 of Presburger arithmetic, born on 2002-07-22, modified 2004-09-14.
	planetmath.org /encyclopedia/PressburgerArithmetic.html (68 words)

	Talk:Presburger arithmetic - Wikipedia, the free encyclopedia
		It would be nice if we knew that the axioms were consistent (and therefore that arithmetic was incomplete), but there is still a possibility of inconsistency.
		On a side note, Presberger arithmetic can be extended to include multiplication by constants (it's just multiple additions, right?), which makes it much more useful for proof of correctness work.
		Well, Presburger arithmetic is defined to include nested quantifier, it is not an extension (the example at the end of the first section correctly points that out by containing some quantifiers).
	en.wikipedia.org /wiki/Talk:Presburger_arithmetic (822 words)

	Encyclopedia :: encyclopedia : Fundamental theorem of arithmetic (Site not responding. Last check: 2007-10-08)
		In mathematics, and in particular number theory, the fundamental theorem of arithmetic or unique factorization theorem is the statement that every positive integer greater than 1 is either a prime number or can be written as a product of prime numbers.
		However if the prime factorizations are not known, the use of Euclid's algorithm generally requires much less calculation than factoring the two numbers.
		The fundamental theorem ensures that additive and multiplicative arithmetic functions are completely determined by their values on the powers of prime numbers.
	www.hallencyclopedia.com /Fundamental_theorem_of_arithmetic (915 words)

	Gödel's incompleteness theorems - Wikipedia, the free encyclopedia
		Gödel demonstrated the incompleteness of a theory of arithmetic, but it is clear that the demonstration could be given for any theory and language of a certain expressiveness.
		For example, first order arithmetic (Peano arithmetic or PA for short) can prove that the largest consistent subset of PA is consistent.
		There are even weaker axiomatic systems that are consistent and complete, for instance Presburger arithmetic which proves every true first-order statement involving only addition.
	en.wikipedia.org /wiki/G%c3%b6del%27s_incompleteness_theorem (4880 words)

	Presburger arithmetic: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-08)
		Presburger arithmetic is the first-order theory[For more, click on this link] of the natural number The number 1 and any other number obtained by adding 1 to it repeatedly
		Again, such a proof cannot be given for general arithmetic; in fact, it follows from Gödel's incompleteness theorem[For more info, click on this link] that general arithmetic cannot be both consistent and complete.
		Presburger arithmetic is an interesting example in computational complexity theory[For more info, click on this link] and computation Problem solving that involves numbers or quantities
	www.absoluteastronomy.com /p/presburger_arithmetic (963 words)

	Citebase - Bounds on the Automata Size for Presburger Arithmetic
		The upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method.
		Boudet, A. and Comon, H. Diophantine equations, Presburger arithmetic and finite automata.
		Gradel, E. Subclasses of Presburger arithmetic and the polynomial-time hierarchy.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:cs/0506008 (964 words)

	On the Automata Size for Presburger Arithmetic (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		In this paper, we prove that the number of states of the minimal deterministic automaton for a Presburger arithmetic formula is triple exponentially bounded in the length of the formula.
		This upper bound is established by comparing the automata for Presburger arithmetic formulas with the...
		11 Presburger arithmetic and finite automata (context) - Boudet, Comon - 1996
	citeseer.ist.psu.edu /663672.html (607 words)

	Citations: Presburger arithmetic and nite automata - Boudet, Comon (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Besides providing a Presburger tool, LASH also included some speci c components to deal with state space exploration, for instance an algorithm for computing (when possible) the....
		Analogous to Presburger arithmetic, we consider the rst order theory of range constraints, which we call Presburger range arithmetic.
		....Presburger Range Arithmetic Analogous to Presburger arithmetic, we consider the rstorder theory of range constraints, which we call Presburger range arithmetic.
	citeseer.ist.psu.edu /context/1744417/0 (1507 words)

	A Comparison of Presburger Engines for EFSM Reachability - Shiple, Kukula, Ranjan (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: Implicit state enumeration for extended finite state machines relies on a decision procedure for Presburger arithmetic.
		While the raw speed of each of these two packages can be superior to the other by a factor of 50 or more, we found the asymptotic performance of Shasta to be equal or superior to that of Omega for the experiments we performed.
		15 Presburger arithmetic and finite automata (context) - Boudet, Comon - 1996
	citeseer.ist.psu.edu /shiple98comparison.html (523 words)

	Learn more about Presburger arithmetic in the online encyclopedia. (Site not responding. Last check: 2007-10-08)
		Learn more about Presburger arithmetic in the online encyclopedia.
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	www.onlineencyclopedia.org /p/pr/presburger_arithmetic.html (517 words)

	Peano Axioms. First Order Arithmetic. By K.Podnieks
		Presburger's proof is a non-trivial piece of mathematics (see Hilbert, Bernays [1934], section 7.4).
		Of course, we must follow the intuition while selecting the axioms of PA. We must follow the intuition when trying to establish formal versions of statements from the usual (intuitive) number theory developed by working mathematicians (as we did it in the Exercise 3.2).
		Generalize the result of the Exercise 1.4 by proving that the set Tr (T) of "arithmetical theorems" of any fundamental formal theory T is computably denumerable.
	www.ltn.lv /~podnieks/gt3.html (7505 words)

	UMCS-87-11-4 Decidability in Temporal Presburger Arithmetic (Site not responding. Last check: 2007-10-08)
		However, this still does not guarantee the existence of a decision method, and it may be necessary to subset the full theory.
		This dissertation contains the identification of a non-trivial subtheory of a temporal theory of Presburger Arithmetic, possessing a decision method.
		The first is a satisfiability procedure based on the algorithm for (non-temporal) Presburger Arithmetic and the second is a tree construction which performs the task required of it, as a result of Konig's Lemma.
	www.cs.man.ac.uk /cstechrep/Abstracts/UMCS-87-11-4.html (209 words)

	Abstraction-based Satisfiability Solving of Presburger Arithmetic - Kroening, Ouaknine, Seshia, Strichman ... (Site not responding. Last check: 2007-10-08)
		Given a Presburger formula , our algorithm invokes a SAT solver to produce proofs of unsatis ability of approximations of .
		These proofs are in turn used to generate abstractions of as inputs to a theorem prover.
		3 A comparison of decision procedures in Presburger arithmetic (context) - Jani, Green et al.
	citeseer.comp.nus.edu.sg /kroening04abstractionbased.html (514 words)

	"Analyzing Automata with Presburger Arithmetic and Uninterpreted Function Symbols"
		We study a class of extended automata defined by guarded commands over Presburger arithmetic with uninterpreted functions.
		On the theoretical side, we show that the bounded reachability problem is decidable in this model.
		On the practical side, the class is useful for modeling programs with potentially infinite data structures, and the reachability procedure can be used for symbolic simulation, testing, and verification.
	www.liafa.jussieu.fr /web9/manifsem/description_en.php?idcongres=221 (105 words)

	Omega: a solver of quantifier-free problems in Presburger Arithmetic (Site not responding. Last check: 2007-10-08)
		Omega: a solver of quantifier-free problems in Presburger Arithmetic
		Chapter 17 Omega: a solver of quantifier-free problems in Presburger Arithmetic
		This is the restriction meaned by ``Presburger arithmetic''.
	pauillac.inria.fr /coq/doc/Reference-Manual020.html (498 words)

	Generic Proof Synthesis for Presburger Arithmetic (Site not responding. Last check: 2007-10-08)
		Generic Proof Synthesis for Presburger Arithmetic --- Draft
		We develop in complete detail an extension of Cooper's decision procedure for Presburger arithmetic that, in the positive case, returns a proof of the input formula.
		The algorithm is formulated as a functional program that makes only very minimal assumptions w.r.t.
	www4.informatik.tu-muenchen.de /~nipkow/pubs/presburger.html (62 words)

	5 Presburger Arithmetic with Uninterpreted Function Symbols (Site not responding. Last check: 2007-10-08)
		The Omega Calculator allows certain restricted uses of uninterpreted function symbols in a Presburger formula.
		Presburger Arithmetic with uninterpreted function symbols is in general undecidable, so in some circumstances we will have to produce approximate results (as we do with the transitive closure operation) [KPRS95].
		The following examples show some legal uses of uninterpreted function symbols in the Omega Calculator:
	www.cs.umd.edu /projects/omega/calculator_doc/node9.html (171 words)

	Proving Safety Properties of Infinite State Systems by Compilation into Presburger Arithmetic. (Site not responding. Last check: 2007-10-08)
		Proving Safety Properties of Infinite State Systems by Compilation into Presburger Arithmetic.
		Abstract: We present in this paper a method combining path decomposition and bottom-up computation features for characterizing the reachability sets of Petri nets within Presburger arithmetic.
		Our implementation is made of a decomposition module and an arithmetic module, the latter being built upon Boudet-Comon's algorithm for solving the decision problem for Presburger arithmetic.
	www.informatik.uni-hamburg.de /TGI/pnbib/f/fribourg_l1.html (158 words)

	Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods
		Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods.
		Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods.
		@inproceedings{BerezinDill2002, author = {Vijay Ganesh,Sergey Berezin and David Dill}, title = {Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods}, booktitle = {FMCAD '02}, year = {2002}, URL = {http://www.gigascale.org/pubs/218.html} }
	www.gigascale.org /pubs/218 (144 words)

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