相关论文: Complexity of short Presburger arithmetic

We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…

A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that…

Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…

We consider expansions of Presburger arithmetic with families of monadic polynomial predicates. (Examples of such predicates are the set of perfect squares, or the set of integers of the form $2n^3-5n+3$, etc.) Although the full attendant…

Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of…

What is the minimum amount of information and time needed to solve 2SAT? When the instance is known, it can be solved in polynomial time, but is this also possible without knowing the instance? Bei, Chen and Zhang (STOC '13) considered a…

We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated…

Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This…

In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free…

We consider Presburger arithmetic extended by the sine function, call this extension sine-Presburger arithmetic ($\sin$-PA), and systematically study decision problems for sets of sentences in $\sin$-PA. In particular, we detail a decision…

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…

We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state…

The constraint satisfaction problem, parameterized by a relational structure, provides a general framework for expressing computational decision problems. Already the restriction to the class of all finite structures forms an interesting…

We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…

We consider an expansion of Presburger arithmetic which allows multiplication by $k$ parameters $t_1,\ldots,t_k$. A formula in this language defines a parametric set $S_\mathbf{t} \subseteq \mathbb{Z}^{d}$ as $\mathbf{t}$ varies in…

Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…

Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…