Decidable first-order theory of the natural numbers with addition
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929. The signature of Presburger arithmetic contains only the addition operation and equality, omitting the multiplication operation entirely. The theory is computably axiomatizable; the axioms include a schema of induction.
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. The asymptotic running-time computational complexity of this algorithm is at least doubly exponential, however, as shown by Fischer & Rabin (1974).
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Presburgerarithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929....
of Peano arithmetic (PA) and primitive recursive arithmetic (PRA), but not to Presburgerarithmetic. Moreover, Gödel's second incompleteness theorem shows...
formulas in Presburgerarithmetic is context-free, every deterministic Turing machine accepting the set of true statements in Presburgerarithmetic has a worst-case...
directly in SMT solvers; see, for instance, the decidability of Presburgerarithmetic. SMT can be thought of as a constraint satisfaction problem and...
theories are algorithmically decidable; examples of this include Presburgerarithmetic, real closed fields, and static type systems of many programming...
addition, which, in this case, is Presburgerarithmetic. Because Presburgerarithmetic is decidable, Skolem arithmetic is also decidable. Ferrante & Rackoff...
Mojżesz Presburger who accomplished his path-breaking work on decidability of the theory of addition (which today is called Presburgerarithmetic) as a...
Mojżesz Presburger showed that the first-order theory of the natural numbers with addition and equality (now called Presburgerarithmetic in his honor)...
double exponential time algorithms include: Decision procedures for Presburgerarithmetic Computing a Gröbner basis (in the worst case) Quantifier elimination...
statement in Presburgerarithmetic requires even more time. Fischer and Rabin proved in 1974 that every algorithm that decides the truth of Presburger statements...
Mojzesz Presburger who accomplished his path-breaking work on decidability of the theory of addition (which today is called Presburgerarithmetic) as a...
in EXPTIME is the problem of proving or disproving statements in Presburgerarithmetic. In some other problems in the design and analysis of algorithms...
expressing the instance as a sentence in Presburgerarithmetic and using the decision procedure for Presburgerarithmetic. The winning-position problem is not...
non-regular. Let us assume that P {\displaystyle P} is definable in PresburgerArithmetic. The predicate P {\displaystyle P} is non regular if and only if...
limits. Dependent ML limits the sort of equality it can decide to Presburgerarithmetic. Other languages such as Epigram make the value of all expressions...
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