Fully　programmable　valve　array　(FPVA)　biochips　have　emerged　as　a　promising　alternative　for　traditional　application-specific　microfluidic　platforms　thanks　to　their　advantages　in　terms　of　flexibility　and　reconfigurability.　By　regularly　deploying　microvalves　along　vertical　and　horizontal　flow　channels,　microfluidic　modules　with　different　sizes　and　shapes　can　be　constructed　dynamically　on　the　chip,　thereby　enabling　the　automatic　execution　of　various　assay　procedures　in　biology　and　biochemistry.　The　above　advantages,　however,　result　largely　from　the　large-scale　integration　of　valves　as　well　as　accurate　control　of　their　switchings,　leading　to　very　complicated　control-logic　design　of　such　chips.　In　this　article,　we　propose　an　reinforcement　learning　(RL)-based　synthesis　flow　for　the　control-logic　design　of　fully　programmable　valve　array　(FPVA)　biochips,　taking　multichannel　switching　and　control-cost　minimization　into　consideration　simultaneously.　By　employing　a　double　deep　Q-network　(DDQN)　and　two　Boolean-logic　simplification　techniques,　control　logics　with　both　high-switching　efficiency　and　low-fabrication　cost　can　be　constructed　automatically.　Furthermore,　the　solution　space　of　multichannel-switching　combinations　is　reduced　to　improve　the　search　efficiency　of　the　proposed　method.　Experimental　results　on　multiple　benchmarks　demonstrate　that　the　proposed　synthesis　flow　leads　to　better-design　solutions　compared　with　the　state-of-the-art　techniques.