Plugin for post list with live search/filtering?

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So I think the simple way of doing this is by creating a post list only showing posts in certain categories, along with a search bar, but the problem I have here is that the search bar opens results in a new page, and shows posts outside of the categories I want it to.

For example, I want the simple list to display restaurants and museums, but not shops. But using the simple solution described above it would open a new page and possibly show results from other categories.

I’m looking for a plugin that allows search results to be live/in-page (maintaining the list format), and posts to be filtered whilst still excluding certain categories. I couldn’t find anything from searching the directory.

Thanks in advance if you have any ideas

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