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11 apr 2018 the proof of decidability of the theory using automata is indeed very nice, but you are right that it is less obviously fruitful than the quantifier.
The proof of decidability of the theory using automata is indeed very nice, but you are right that it is less obviously fruitful than the quantifier elimination procedure for two reasons: firstly, as you point out, the justification of the quantifier elimination procedure is proof-theoretic rather than semantic and so you can conclude from it that the axiomatic system of presburger arithmetic is complete; secondly, the quantifier elimination procedure gives useful information about the sets.
Decidability and complexity issues for fragments of ltl with presburger constraints obtained by restricting the syntactic resources of the formulae.
The first-order theory of addition over the natural numbers, known as presburger arith- metic, is decidable in double exponential time.
I the decidability of presburger arithmetic can also be proved usingautomata. I stronger result: we can prove decidability of certain extensions of presburger arithmetic.
3 mar 2017 abstract: the first-order theory of addition over the natural numbers, known as presburger arithmetic, is decidable in double exponential time.
The award is named after mojżesz presburger who accomplished his path-breaking work on decidability of the theory of addition (which today is called presburger arithmetic) as a student in 1929. Past recipients of the award are: mikołaj bojańczyk (2010) patricia bouyer-decitre (2011) venkatesan guruswami and mihai pătraşcu (2012).
Y+ is commonly called the theory of integers under addition or presburger arithmetic. Presburger [6] proved that y+ is decidable, that is, that 9-f is recursive.
A 22:` upper bound on the complexity of presburger anthmeuc j comptr syst scl 16, 3 (june 1978), 323-332 google scholar 11 shostak, r e an eff~oent decision procedure for arithmetic w~th function symbols sri teeh rep csl- 65, stanford research insatute, menlo park, cahf, 1977, also presented at workshop on automatic deductions, cambridge, mass.
Work on decidability of the theory of addition (which today is called presburger arithmetic) as a student a brief history of the presburger award follows below.
Presburger arithmetic is much weaker than peano arithmetic, which includes both addition and multiplication operations. Unlike peano arithmetic, presburger arithmetic is a decidable theory. This means it is possible to algorithmically determine, for any sentence in the language of presburger arithmetic, whether that sentence is provable from the axioms of presburger arithmetic.
However, presburger arithmetic is decidable in contrast to peano arithmetic. ‚erefore, a number of decision procedures exists that decide for all pres-burger formulae mojzesz presburger showed that his logic is decidable [19] by proving that it ad-˙ mits quanti•er elimination.
Presburger logic is the decidable rst-order theory of natural numbers. Presburger formulas use variables, constants, addition and subtraction, comparisons, and quanti cation. The class of counter systems where the guards as well as actions are represented using presburger for-mulas are called presburger counter systems.
We recall that presburger arithmetic (presburger, 1929) is the first-order theory of integers with addition (but without multiplication) and, it can be shown to be decidable by quantifiers elimination.
Where fij and gij are linear functions with integer coefficients and ϕi, are pres- burger formulas with x and z free.
Decidability proof of presburger arithmetic the first-order theory of the natural numbers is undecidable.
It is consistent, complete, and decidable, but is not strong enough to form statements about multiplication.
The proof of decidability of the theory using automata is indeed very nice, but you are right that it is less obviously fruitful than the quantifier elimination procedure for two reasons: firstly, as you point out, the justification of the quantifier elimination procedure is proof-theoretic rather than semantic and so you can conclude from it that the axiomatic system of presburger arithmetic.
12 jul 2006 because it works by a reduction to pa, our algorithm yields the decidability of a combination of sets of uninterpreted elements with any decidable.
We prove several decidability and undecidability results for the satisfiability and validity problems for and presburger arithmetic is known to be decidable [22].
The decidability of presburger arithmetic [27], the first-order theory of the integers with addition, is a fundamental result that has wide-ranging applications in formal verification and automated deduction. A natural extension of presburger arithmetic is obtained by adding a binary divisibility predicate.
These are presburger counter systems defined over flat control graphs with arcs labelled by transition functions de-fined by presburger formulae, for which counting iteration o ver every cycle in the control graph is presburger definable.
30 may 2014 while it can't define prime numbers or division by variables, it is complete and decidable.
Which include the standard interpretation of presburger arithmetic.
1 decidability of presburger arithmetic using finite automata presented by shubha jain reference paper by alexandre boudet and hubert.
16 feb 2021 we show that the first-order theory of sturmian words over presburger arithmetic is decidable.
Decidable formalisms for quantitative languages and objectives the most expressive known class of wa enjoying decidability is that of finitely ambiguous wa [13],.
We also show decidability of reachabil-ity for parametric one-counter automata by reduction to existential presburger arithmetic with divisibility [17]. We defer consideration of the complexity of the latter problem to the full version of this paper.
We will show that presburger arithmetic is decidable (can be solved by an algorithm), using an algorithm that represents the truth of formulas as finite automata. In order to show that true arithmetic is undecidable, we propose a formal definition of algorithm: the turing machine.
Our decidability results about cltl(dl) fragments restricting the syntactic ressources of formulas are optimal with respect to the constraints used. Satis-fiability for ltl with quantifier-free presburger constraints (properly including difference constraints) is undecidable even if restricted to x-length one and to one counter.
Since presburger arithmetic is know to be decidable in double exponential space. In [wb95] it was suggested to use concurrent automata as a representation. This indeed reduces the size of the automata, but pushes up the complexity of manipulating them.
The award is named after mojzesz presburger, who accomplished his work on decidability of the theory of addition (which today is called presburger arithmetic) as a student in 1929. Demaine will be presented with the presburger award at the annual international colloquium on automata, languages and programming (icalp), held in latvia in july.
Decidability of symbolic heaps with inductive de nitions and arithmetic. Section 2 de nes the system sla1 and its semantics, and shows the unde-cidability. Section 3 proposes the decidable subsystem dpi of presburger arith-metic with inductive de nitions, and proves its decidability.
Logic (definability and decidability issues); finite automata and formal arithmétique de presburger et arithmétique de skolem, université paris 7, 1996.
The validity of presburger arithmetic formulas is decidable, and then it is decidable whether scan tile the nonnegative integer orthant n 2 of the cartesian plane.
As for the other point, what i meant is that an arbitrary sentence formulated in the language of presburger arithmetic is not decidable in first order logic with no assumptions, although it is decidable whether or not it follows from the axioms of presburger arithmetic(pa l- s is decidable, l- pa - s is decidable, l- s is not decidable).
Using an automata-theoretic approach, we investigate the decidability of liveness properties (called presburger liveness properties) for timed automata when presburger formulas on configurations are allowed.
Decidability of the rst-or der theory of knuth-bendix order, thereby solving a long-standing open problem in term rewriting (o cially listed as rta open problem 99 since 2000). This decidability result is obtained by quantier elimination on a complex structure containing term algebras and presburger arithmetic.
Presburger award for young scientists 2021 - call for nominations. The presburger award recognises outstanding contributions by a young scientist in theoretical computer science, documented by a published paper or a series of published papers. It is named after mojzesz presburger who accomplished his ground-breaking work on decidability of the theory of addition (known today as presburger arithmetic) as a student in 1929.
7 jan 2020 keywords: presburger arithmetic, büchi arithmetic, reachability, automatic decidability and complexity results for an extension of presburger.
These results have been used to prove decidability of rst-order or mso theories. Buc hi knew that automata and presburger arithmetic (the rst-order theory of the natural numbers with addition) are closely connected. He used automata to give a simple (non quanti er elimination) proof of the decidability of presburger arithmetic.
Give a much simplified proof of the decidability of two-variable logics for data words with the successor and data-equality predicates. In addition, the new proof provides several new fragments of lower complexity. The proof mixes database-inspired constraints with encodings in presburger arithmetic.
This extends the earlier decidability result for plain bpp as well as decidability for timed bpp with strictly positive durations of actions both ill-timed and well-timed semantics are treated. Our decision procedure is based on decidability of the validity problem for presburger arithmetic.
Presburger's essay on the completeness and decidability of arithmetic with integer addition but without multiplication is a milestone in the history of mathematical logic and formal metatheory. The proof is constructive, using tarski-style quantifier elimination and a four-part recursive comprehension principle for axiomatic consequence.
14 jun 1977 result is that the validity of unquantifled formulas in presburger array theory is decidable, yet quantified formulas irs general are undecidable.
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