Linear Ranking for Linear Lasso Programs
نویسندگان
چکیده
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and an invariant. We present the— to the best of our knowledge—first method to synthesize termination arguments for lasso programs that uses linear arithmetic. We prove a completeness theorem. The completeness theorem establishes that, even though we use only linear (as opposed to non-linear) constraint solving, we are able to compute termination arguments in several interesting cases. The key to our method lies in a constraint transformation that replaces a disjunction by a sum.
منابع مشابه
Ranking Function Synthesis for Linear Lasso Programs
The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting invariants. We extend existing methods in several ways. First, we use Motzkin’s Transposition Theorem instead of Farkas’ Lemma. This allows us to consider linear l...
متن کاملThe Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem is known to be in coNP when variables range over the integers and in PTIME for the rational numbers, or real numbers. Here we show that deciding whether a l...
متن کاملDifferenced-Based Double Shrinking in Partial Linear Models
Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...
متن کاملGeometric Series as Nontermination Arguments for Linear Lasso Programs
We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument. A geometric nontermination argument is a finite representation of an infinite execution of the form (~x+ ∑t i=0 λ~y)t≥0. The existence of this nontermination argument can be stated as a set of nonlinear algebraic constraints. We show that every linear loop program that has a bou...
متن کاملA Parametric Simplex Approach to Statistical Learning Problems
In this paper, we show that the parametric simplex method is an efficient algorithm for solving various statistical learning problems that can be written as linear programs parametrized by a so-called regularization parameter. The parametric simplex method offers significant advantages over other methods: (1) it finds the complete solution path for all values of the regularization parameter by ...
متن کامل