Will Birch gives a thoughtful critique of Open Theism:

The Psalmist continues: “Before a word is on my tongue you, LORD, know it completely.” (Ps. 139:4) My opinion is that this verse challenges the notion of Open Theism. For God cannot, in Open theory, but predict what I might say, given His knowledge of my character, and given His acquaintance with the varying situations I may encounter and how I may react. But here, the Psalmist indicates that God knows completely, yada’ta chullah, knows the whole of my speech. But notice, too, that God’s knowledge of my words is prior to the actual speaking of those words. Notice, as well, that His foreknowledge of my words is complete and exhaustive.

The passage being referenced in Psalms is not as cut and dry and Birch would like. Speech does not work mechanically where one can just view isolated sentences and determine absolute meaning. Even if King David says that God knows His thoughts “completely”, this falls within the bound of normal hyperbolic speech. And if King David’s point is that his relationship with God is unique, this actually works against what Birch is attempting to gain from this passage. Context is what will inform the reader on King David’s meaning.

Surveying the rest of the chapter shows that King David believes God knows him by searching him.

Psa 139:1 To the choirmaster. A Psalm of David. O LORD, you have searched me and known me!

King David ends this psalm with a challenge to God to search him to know his heart:

Psa 139:23 Search me, O God, and know my heart! Try me and know my thoughts!
Psa 139:24 And see if there be any grievous way in me, and lead me in the way everlasting!

King David believes that God learns about David through trials. For God to know if King David will remain true, God puts David into situations. This, in itself, undermines the point Birch makes.