Conditional @HostBinding depending on @Input()

What you did is almost correct :

export class MyComponent {
    @Input()
    public input: string;

    @HostBinding('class.foo')
    public get isFoo(): Boolean {
        return this.input !== 'not correct';
    }

}

Try this way. Make @Input property getter/setter and set the isFoo from the setter.

export class MyComponent {   
     @Input()
        public get input (): string {
          return this._input;
        }
        public set input (val: string) {
          this._input = val;
          // when the input is set check it and set isFoo;
          this.isFoo = (val != 'not correct');
        }

        @HostBinding('class.foo')
        public isFoo: Boolean = false; // false is init value

        constructor() {
        }
    }