We introduce the framework of the left-hand side restricted promise constraint satisfaction problem, which includes problems like approximating clique number of a graph. We study the parameterized complexity of problems in this class and provide some initial results. The main technical contribution is a sufficient condition for W[1]-hardness which, in particular, covers left-hand side restricted bounded arity CSPs.

翻译：我们引入了左侧受限承诺约束满足问题的框架，该框架涵盖了诸如近似图团数等问题。我们研究了该类中问题的参数化复杂性，并给出了一些初步结果。主要的技术贡献是提出了一个W[1]难度的充分条件，该条件特别涵盖了左侧受限有元数CSP问题。