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，该框架包含诸如近似图团数等问题。我们研究了此类问题的参数化复杂性，并提供了一些初步结果。主要技术贡献在于给出了W[1]-难解性的充分条件，该条件特别涵盖了左侧受限有界元数CSP。