A　new　concept　of　center　processing　unit　(CPU)-integrated　simultaneously　transmitting　and　reflecting　reconfigurable　intelligent　surface　(STAR-RIS)　is　proposed,　namely　computing　STAR-RIS.　Computation-intensive　and　delay-sensitive　tasks　from　mobile　users　can　be　partially　processed　at　the　computing　STAR-RIS.　We　aim　to　minimize　the　energy　consumption　of　users　and　the　computing　STAR-RIS,　and　formulate　a　joint　task　offloading　and　transmission　resource　allocation　problem.　The　solution　of　this　problem　is　affected　by　the　offloading　decision　and　the　amplitude　and　phase-shift　of　the　computing　STAR-RIS.　To　solve　the　non-convex　problem,　we　decompose　it　into　two　subproblems:　1)　For　the　task　offloading　subproblem,　the　offloading　decision　is　optimized　utilizing　the　Karush-Kuhn-　Tucker　(KKT)　conditions;　and　2)　For　the　transmission　resource　allocation　subproblem,　the　transmission-reflection　coefficient　matrix　are　optimized　via　successive　convex　approximation　(SCA).　Simulation　results　show　that　our　proposed　algorithm　can　converge　faster　and　have　lower　energy　consumption　than　the　conventional　STAR-RIS.　©　2024　IEEE.