diff --git a/src/tables/instruction.rs b/src/tables/instruction.rs
index fbb85f4..6505f6c 100644
--- a/src/tables/instruction.rs
+++ b/src/tables/instruction.rs
@@ -83,7 +83,8 @@ impl InstructionTable {
         }
     }
 
-    pub fn extend_column(&mut self, rand_field_elem: u128, challenges: Vec<FieldElement>) {
+    pub fn extend_column(&mut self, rand_field_elem: u128, challenges: Vec<FieldElement>) ->Vec<FieldElement>{
+        let mut terminal:Vec<FieldElement>=Vec::new();
         let mut ppa = self.table.matrix[0 as usize][Indices::Address as usize]
         * challenges[ChallengeIndices::A as usize]
         + self.table.matrix[0 as usize][Indices::CurrentInstruction as usize]
@@ -120,7 +121,11 @@ impl InstructionTable {
                 self.table.matrix[(i + 1) as usize][Indices::EvaluationArg as usize] =
                     pea * challenges[ChallengeIndices::Eta as usize] + weighted_sum;
             }
+           
         }
+        terminal.push(ppa);
+        terminal.push(pea);
+        terminal
     }
 
     pub fn generate_air(&self, challenges: Vec<FieldElement>,tppa:FieldElement,tpea:FieldElement) -> Vec<Polynomial> {
diff --git a/src/tables/io.rs b/src/tables/io.rs
index ba509a5..7908cab 100644
--- a/src/tables/io.rs
+++ b/src/tables/io.rs
@@ -38,7 +38,7 @@ impl IOTable {
 
     pub fn pad(&mut self) {}
 
-    pub fn extend_column_ea(&mut self, rand_field_elem: u128, challenge: FieldElement) {
+    pub fn extend_column_ea(&mut self, rand_field_elem: u128, challenge: FieldElement)->Vec<FieldElement> {
         let mut ea = FieldElement::new(rand_field_elem, self.table.field); // take rand_field_elem as zero if no random secret implementation
         self.table.matrix[0][1] = ea;
         for i in 0..self.table.length - 1 {
@@ -47,7 +47,12 @@ impl IOTable {
             self.table.matrix[(i + 1) as usize][1] = ea;
             //Tea = IOTable.matrix[length-1][1]
         }
+        let mut terminal: Vec<FieldElement>=Vec::new();
+        terminal.push(ea);
+        terminal
+
     }
+
 }
 
 #[cfg(test)]
diff --git a/src/tables/memory.rs b/src/tables/memory.rs
index c23971c..3711e06 100644
--- a/src/tables/memory.rs
+++ b/src/tables/memory.rs
@@ -105,7 +105,8 @@ impl MemoryTable {
     }
 
     //the matrix taken here is padded
-    pub fn extend_column_ppa(&mut self, rand_field_elem: u128, challenges: Vec<FieldElement>) {
+    pub fn extend_column_ppa(&mut self, rand_field_elem: u128, challenges: Vec<FieldElement>)->Vec<FieldElement> {
+        let mut terminal:Vec<FieldElement>= Vec::new();
         let mut ppa = FieldElement::new(rand_field_elem, self.table.field);
         self.table.matrix[0][Indices::PermutationArg as usize] = ppa;
         for i in 0..self.table.length - 1 {
@@ -118,7 +119,18 @@ impl MemoryTable {
                 - challenges[ChallengeIndices::Beta as usize];
             ppa *= weighted_sum;
             self.table.matrix[(i + 1) as usize][Indices::PermutationArg as usize] = ppa;
+
         }
+        let mut tppa=ppa*(self.table.matrix[self.table.length as usize][Indices::Cycle as usize]
+            * challenges[ChallengeIndices::D as usize]
+            + self.table.matrix[self.table.length as usize][Indices::MemoryPointer as usize]
+                * challenges[ChallengeIndices::E as usize]
+            + self.table.matrix[self.table.length as usize][Indices::MemoryValue as usize]
+                * challenges[ChallengeIndices::F as usize]
+            - challenges[ChallengeIndices::Beta as usize]);
+            let mut Tppa:Vec<FieldElement>=Vec::new();
+            Tppa.push(tppa);
+            Tppa
     }
 
     //this is after padding and extension
diff --git a/src/tables/processor.rs b/src/tables/processor.rs
index f9fe252..e43d7e4 100644
--- a/src/tables/processor.rs
+++ b/src/tables/processor.rs
@@ -129,7 +129,7 @@ impl ProcessorTable {
     }
 
     //the matrix taken here is padded
-    pub fn extend_columns(&mut self, challenges: Vec<FieldElement>) {
+    pub fn extend_columns(&mut self, challenges: Vec<FieldElement>)->Vec<FieldElement> {
         //@todo Note: Taking init 1 for now, change to random secret initial value which we check by difference constraint of tmpa = Tppa
         let mut ipa = FieldElement::one(self.table.field);
         let mut mpa = FieldElement::one(self.table.field);
@@ -153,6 +153,13 @@ impl ProcessorTable {
             ipa *= weighted_sum;
             self.table.matrix[(i + 1) as usize][Indices::InstructionPermutaion as usize] = ipa;
         }
+        let mut tipa=ipa*(self.table.matrix[self.table.length as usize][Indices::InstructionPointer as usize]
+            * challenges[ChallengeIndices::A as usize]
+            + self.table.matrix[self.table.length as usize][Indices::CurrentInstruction as usize]
+                * challenges[ChallengeIndices::B as usize]
+            + self.table.matrix[self.table.length as usize][Indices::NextInstruction as usize]
+                * challenges[ChallengeIndices::C as usize]
+            - challenges[ChallengeIndices::Alpha as usize]);
 
         for i in 0..self.table.length - 1 {
             let weighted_sum = self.table.matrix[i as usize][Indices::Cycle as usize]
@@ -165,6 +172,13 @@ impl ProcessorTable {
             mpa *= weighted_sum;
             self.table.matrix[(i + 1) as usize][Indices::MemoryPermuation as usize] = mpa;
         }
+        let mut tmpa=mpa*(self.table.matrix[self.table.length as usize][Indices::Cycle as usize]
+            * challenges[ChallengeIndices::D as usize]
+            + self.table.matrix[self.table.length as usize][Indices::MemoryPointer as usize]
+                * challenges[ChallengeIndices::E as usize]
+            + self.table.matrix[self.table.length as usize][Indices::MemoryValue as usize]
+                * challenges[ChallengeIndices::F as usize]
+            - challenges[ChallengeIndices::Beta as usize]);
 
         let f =
             |x: char| -> FieldElement { FieldElement::new((x as u32) as u128, self.table.field) };
@@ -189,6 +203,14 @@ impl ProcessorTable {
                 self.table.matrix[(i + 1) as usize][Indices::OutputEvaluation as usize] = oea;
             }
         }
+        let mut tiea=iea;
+        let mut toea =oea;
+        let mut terminal:Vec<FieldElement>=Vec::new();
+        terminal.push(tipa);
+        terminal.push(tmpa);
+        terminal.push(tiea);
+        terminal.push(toea);
+        terminal
     }
 
     pub fn generate_zerofier(&self) -> Vec<Polynomial> {