An Automata-Theoretic Algorithm for Counting Solutions to Presburger Formulas
نویسندگان
چکیده
We present an algorithm for counting the number of integer solutions to selected free variables of a Presburger formula. We represent the Presburger formula as a deterministic finite automaton (DFA) whose accepting paths encode the standard binary representations of satisfying free variable values. We count the number of accepting paths in such a DFA to obtain the number of solutions without enumerating the actual solutions. We demonstrate our algorithm on a suite of eight problems to show that it is universal, robust, fast, and scalable.
منابع مشابه
On Presburger Liveness of Discrete Timed Automata
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. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness...
متن کاملCounting in trees
We consider automata and logics that allow to reason about numerical properties of unranked trees, expressed as Presburger constraints. We characterize non-deterministic automata by Presburger Monadic Second-Order logic, and deterministic automata by Presburger Fixpoint logic. We show how our results can be used in order to obtain efficient querying algorithms on XML trees.
متن کاملConstrained Properties, Semilinear Systems, and Petri Nets
We investigate the veriication problem of two classes of innnite state systems w.r.t. nonregular properties (i.e., nondeenable by nite-state !-automata). The systems we consider are Petri nets as well as semilinear systems including push-down systems and PA processes. On the other hand, we consider properties ex-pressible in the logic CLTL which is an extension of the linear-time temporal logic...
متن کاملLeast Significant Digit First Presburger Automata
1 Introduction Presburger arithmetic [Pre29] is a decidable logic used in a large range of applications. As described in [Lat04], this logic is central in many areas including integer programming problems [Sch87], compiler optimization techniques [Ome], program analysis tools [BGP99, FO97, Fri00] and model-checking [BFL04, Fas, Las]. Different techniques [GBD02] and tools have been developed fo...
متن کاملAn Automata - Theoretic Approach toPresburger Arithmetic Constraints
This paper introduces a nite-automata based representation of Presburger arithmetic deenable sets of integer vectors. The representation consists of concurrent automata operating on the binary en-codings of the elements of the represented sets. This representation has several advantages. First, being automata-based it is operational in nature and hence leads directly to algorithms, for instance...
متن کامل