diff --git a/state-machines/arith/pil/arith_table.pil b/state-machines/arith/pil/arith_table.pil
index 53f8b238..c238258a 100644
--- a/state-machines/arith/pil/arith_table.pil
+++ b/state-machines/arith/pil/arith_table.pil
@@ -266,7 +266,7 @@ airtemplate ArithTable(int N = 2**7, int generate_table = 0) {
     }
     col witness multiplicity;
 
-    lookup_proves(ARITH_TABLE_ID, mul: multiplicity, cols: [OP, FLAGS, RANGE_AB, RANGE_CD]);
+    lookup_proves(ARITH_TABLE_ID, mul: multiplicity, expressions: [OP, FLAGS, RANGE_AB, RANGE_CD]);
 }
 
 function arith_table_assumes( const expr op, const expr flag_m32, const expr flag_div, const expr flag_na,
@@ -275,9 +275,9 @@ function arith_table_assumes( const expr op, const expr flag_m32, const expr fla
                               const expr flag_main_mul, const expr flag_main_div, const expr flag_signed,
                               const expr range_ab, const expr range_cd) {
 
-    lookup_assumes(ARITH_TABLE_ID, cols: [ op, flag_m32 + 2 * flag_div + 4 * flag_na + 8 * flag_nb +
-                                           16 * flag_np + 32 * flag_nr + 64 * flag_sext +
-                                           128 * flag_div_by_zero + 256 * flag_div_overflow +
-                                           512 * flag_main_mul + 1024 * flag_main_div + 2048 * flag_signed,
-                                           range_ab, range_cd]);
+    lookup_assumes(ARITH_TABLE_ID, expressions: [ op, flag_m32 + 2 * flag_div + 4 * flag_na + 8 * flag_nb +
+                                                  16 * flag_np + 32 * flag_nr + 64 * flag_sext +
+                                                  128 * flag_div_by_zero + 256 * flag_div_overflow +
+                                                  512 * flag_main_mul + 1024 * flag_main_div + 2048 * flag_signed,
+                                                  range_ab, range_cd]);
 }
diff --git a/state-machines/binary/pil/binary_extension.pil b/state-machines/binary/pil/binary_extension.pil
index 13681fc1..815d18cd 100644
--- a/state-machines/binary/pil/binary_extension.pil
+++ b/state-machines/binary/pil/binary_extension.pil
@@ -104,5 +104,5 @@ airtemplate BinaryExtension(const int N = 2**18, const int operation_bus_id) {
         multiplicity
     );
 
-    range_check(colu: in2[0], min: 0, max: 2**24-1, sel: op_is_shift);
+    range_check(expression: in2[0], min: 0, max: 2**24-1, sel: op_is_shift);
 }
diff --git a/state-machines/main/pil/main.pil b/state-machines/main/pil/main.pil
index 6d8d7506..1352aab1 100644
--- a/state-machines/main/pil/main.pil
+++ b/state-machines/main/pil/main.pil
@@ -1,6 +1,6 @@
 require "std_lookup.pil"
 require "std_permutation.pil"
-require "std_common.pil"
+require "std_direct.pil"
 
 const int BOOT_ADDR = 0x1000;
 const int END_PC_ADDR = 0x2000;
@@ -163,7 +163,7 @@ airtemplate Main(int N = 2**21, int RC = 2, int stack_enabled = 0, const int ope
     // Operation.assume => how organize software
     col witness __debug_operation_bus_enabled;
 
-    lookup_assumes(operation_bus_id, [STEP, op, a[0], (1 - m32) * a[1], b[0], (1 - m32) * b[1], ...c, flag], sel: is_external_op * __debug_operation_bus_enabled, name: PIOP_NAME_ISOLATED);
+    lookup_assumes(operation_bus_id, [STEP, op, a[0], (1 - m32) * a[1], b[0], (1 - m32) * b[1], ...c, flag], sel: is_external_op * __debug_operation_bus_enabled);
 
     const expr a_src_c;
     const expr b_src_c;
@@ -241,8 +241,8 @@ airtemplate Main(int N = 2**21, int RC = 2, int stack_enabled = 0, const int ope
     //
 
     const expr bus_main_segment = main_segment - SEGMENT_LAST * (main_segment * main_last_segment - 1 + main_last_segment);
-    permutation (MAIN_CONTINUATION_ID, cols: [bus_main_segment, is_last_continuation, pc, c[0], c[1], set_pc, jmp_offset1, flag * SEGMENT_LAST * (jmp_offset1 - jmp_offset2) + jmp_offset2],
-                                        sel: SEGMENT_LAST - SEGMENT_L1, name: PIOP_NAME_ISOLATED, bus_type: PIOP_BUS_SUM);
+    permutation (MAIN_CONTINUATION_ID, expressions: [bus_main_segment, is_last_continuation, pc, c[0], c[1], set_pc, jmp_offset1, flag * SEGMENT_LAST * (jmp_offset1 - jmp_offset2) + jmp_offset2],
+                                               sel: SEGMENT_LAST - SEGMENT_L1, bus_type: PIOP_BUS_PROD);
 
     flag * (1 - flag) === 0;
 
@@ -271,6 +271,6 @@ airtemplate Main(int N = 2**21, int RC = 2, int stack_enabled = 0, const int ope
     lookup_assumes(ROM_BUS_ID, [pc, a_offset_imm0, a_imm1, b_offset_imm0, b_imm1, ind_width,
                                 op, store_offset, jmp_offset1, jmp_offset2, rom_flags], sel: 1 - SEGMENT_L1);
 
-    direct_global_update_proves(MAIN_CONTINUATION_ID, cols: [0, 0, 4096, 0, 0, 0, 0, 0], bus_type: PIOP_BUS_SUM);
-    direct_global_update_assumes(MAIN_CONTINUATION_ID, cols: [0, 1, 0x1000_0000, 0, 0, 0, 0, 0], bus_type: PIOP_BUS_SUM);
+    direct_global_update_proves(MAIN_CONTINUATION_ID, expressions: [0, 0, 4096, 0, 0, 0, 0, 0], bus_type: PIOP_BUS_PROD);
+    direct_global_update_assumes(MAIN_CONTINUATION_ID, expressions: [0, 1, 0x1000_0000, 0, 0, 0, 0, 0], bus_type: PIOP_BUS_PROD);
 }
\ No newline at end of file
diff --git a/state-machines/mem/pil/mem.pil b/state-machines/mem/pil/mem.pil
index 27052d91..4788bdd1 100644
--- a/state-machines/mem/pil/mem.pil
+++ b/state-machines/mem/pil/mem.pil
@@ -153,10 +153,10 @@ airtemplate Mem(const int N = 2**21, const int id = MEMORY_ID, const int RC = 2,
     direct_global_update_proves(MEMORY_CONT_ID, [ base_address, 0, internal_base_address, 0, ...zeros], sel: enable_flag);
 
     // for security check that first address has correct value, to avoid add huge quantity of instances to "overflow" prime field.
-    range_check(colu: previous_segment_addr - internal_base_address + 1, min: 1, max: MEMORY_MAX_DIFF);
+    range_check(expression: previous_segment_addr - internal_base_address + 1, min: 1, max: MEMORY_MAX_DIFF);
 
     // control final of memory
-    range_check(colu: internal_end_address - segment_last_addr + 1, min: 1, max: MEMORY_MAX_DIFF);
+    range_check(expression: internal_end_address - segment_last_addr + 1, min: 1, max: MEMORY_MAX_DIFF);
 
 
     // check increment of memory
@@ -181,7 +181,7 @@ airtemplate Mem(const int N = 2**21, const int id = MEMORY_ID, const int RC = 2,
 
         is_first_segment * SEGMENT_L1 * (1 - addr_changes) === 0;
 
-        range_check(colu: increment, min: 1, max: MEMORY_MAX_DIFF);
+        range_check(expression: increment, min: 1, max: MEMORY_MAX_DIFF);
     }
 
     (1 - addr_changes) * (addr - previous_addr) === 0;
@@ -218,7 +218,7 @@ airtemplate Mem(const int N = 2**21, const int id = MEMORY_ID, const int RC = 2,
     // These are handled with the Memory Align component
 
     const expr mem_op = wr * (MEMORY_STORE_OP - MEMORY_LOAD_OP) + MEMORY_LOAD_OP;
-    permutation_proves(MEMORY_ID, cols: [mem_op, addr * mem_bytes, step, mem_bytes, ...value], sel: sel);
+    permutation_proves(MEMORY_ID, expressions: [mem_op, addr * mem_bytes, step, mem_bytes, ...value], sel: sel);
 }
 
 function mem_load(int id = MEMORY_ID, expr addr, expr step, expr step_offset = 0, expr bytes = 8, expr value[], expr sel = 1) {
diff --git a/state-machines/mem/pil/mem_align.pil b/state-machines/mem/pil/mem_align.pil
index 8a23ab2a..dae9a47a 100644
--- a/state-machines/mem/pil/mem_align.pil
+++ b/state-machines/mem/pil/mem_align.pil
@@ -184,5 +184,5 @@ airtemplate MemAlign(const int N = 2**10, const int RC = 2, const int CHUNK_NUM
     for (int i = 0; i < RC; i++) {
         value[i] === sel_prove * prove_val[i] + sel_assume * assume_val[i];
     } 
-    permutation(MEMORY_ID, cols: [wr * (MEMORY_STORE_OP - MEMORY_LOAD_OP) + MEMORY_LOAD_OP, addr * CHUNK_NUM + offset, step, width, ...value], sel: sel_prove - sel_assume);
+    permutation(MEMORY_ID, expressions: [wr * (MEMORY_STORE_OP - MEMORY_LOAD_OP) + MEMORY_LOAD_OP, addr * CHUNK_NUM + offset, step, width, ...value], sel: sel_prove - sel_assume, bus_type: PIOP_BUS_PROD);
 }
\ No newline at end of file