Smooth and sharp thresholds for random k-XOR-CNF satisfiability
نویسندگان
چکیده
The aim of this paper is to study the threshold behavior for the satisfiability property of a random k-XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with k variables per equation. For k ≥ 3 we show the existence of a sharp threshold for the satisfiability of a random k-XOR-CNF formula, whereas there are smooth thresholds for k = 1 and k = 2. Mathematics Subject Classification. 05C80, 68R05, 60C05.
منابع مشابه
Combining the k-CNF and XOR Phase-Transitions
The runtime performance of modern SAT solvers on random k-CNF formulas is deeply connected with the ‘phase-transition’ phenomenon seen empirically in the satisfiability of random k-CNF formulas. Recent universal hashing-based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both k-CNF and XOR constraints (...
متن کاملThe Hard Problems Are Almost Everywhere For Random CNF-XOR Formulas
Recent universal-hashing based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both CNF constraints and variable-width XOR constraints (known as CNF-XOR formulas). In this paper, we present the first study of the runtime behavior of SAT solvers equipped with XOR-reasoning techniques on random CNF-XOR form...
متن کاملApproximating The Satisfiability Threshold For Random K-Xor-Formulas
In this paper we study random linear systems with k variables per equation over the finite field GF (2), or equivalently k-XOR-CNF formulas. In a previous paper Creignou and Daudé proved that the phase transition for the consistency (satisfiability) of such systems (formulas) exhibits a sharp threshold. Here we prove that the phase transition occurs as the number of equations (clauses) is propo...
متن کاملOn Sharp Thresholds in Random Geometric Graphs
We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for satisfiability.
متن کاملXOR Satisfiability Solver Module for DPLL Integration
Satisfiability solvers that are based on the Davis-Putnam-Logemann-Loveland (DPLL) algorithm operate on propositional logic formulas in conjunctive normal form (CNF). Despite major improvements in solver technology, using only CNF does not seem to scale well for problem instances involving XOR expressions. We present a decision procedure to determine effectively the satisfiability of XOR clause...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- ITA
دوره 37 شماره
صفحات -
تاریخ انتشار 2003