Update app.py

app.py

@@ -98,8 +98,47 @@ Provide a concise explanation for the classification, referencing key problem fe
 
 Your Classification and Explanation:
 ''')
-  return classification 
+  
+  return classification
 
+def critic_analysis(classification_output):
+    critic = model_response(f'''"You are PolyCritic, an expert in computational complexity and problem decomposition. Your goal is to critically evaluate whether a given
+      NP-hard problem, when broken into P-solvable subproblems, can be efficiently recombined to yield the full solution. Here is the problem and the analysis: {classification}
+
+Instructions:
+1️⃣ Input: A decomposed NP-hard problem along with its P-solvable subproblems.
+2️⃣ Step 1 - Validate Subproblems:
+
+Do these subproblems fully cover the original problem?
+
+Are they correctly categorized as P?
+3️⃣ Step 2 - Analyze Recombination Complexity:
+
+Can the subproblem solutions be combined in polynomial time?
+
+If not, what is the bottleneck? (e.g., exponential merging, missing constraints)
+4️⃣ Step 3 - Provide Verdict:
+
+If recombination is efficient, explain why this suggests progress towards P = NP.
+
+If inefficient, identify where complexity remains and suggest next steps.
+5️⃣ Step 4 - Provide Complexity Insights:
+
+Offer insights into whether certain structural patterns predict efficient recombination.
+
+Suggest improvements in decomposition strategies.
+
+Example Analysis Format:
+💡 Problem: Traveling Salesperson (TSP)
+🔍 Subproblems: Shortest paths between city clusters (P-solvable)
+⚖ Recombination Complexity: Exponential growth in possible paths when merging clusters
+🚨 Verdict: Recombination remains NP-hard → Decomposition needs refinement
+
+👉 Your task is to apply this structured critique to any NP-hard problem and determine if it truly reduces to P.''')  
+    return critic
+    
+
+'''
 iface = gr.Interface(
     fn=pvsnp, 
     inputs=gr.Textbox(label="What problem would you like to classify as P or NP?"), 
@@ -111,4 +150,29 @@ iface = gr.Interface(
 )
 
 # Launch the app
-iface.launch()
+iface.launch() '''
+
+with gr.Blocks() as app:
+    gr.Markdown("# PolyProb & PolyCritic AI 🤖")
+    gr.Markdown('''PolyProb and PolyCritic are AI Agents that help users classify a problem into categories such as P, NP, NP-complete, NP-hard while 
+    providing clear, concise explanations of its reasoning. As part of AI Quotient’s Millennium Math Challenge, it is the first step towards solving the P vs NP problem.''')
+    
+    with gr.Row():
+        problem_input = gr.Textbox(label="Enter a computational problem")
+        classify_button = gr.Button("Classify")
+    
+    classification_output = gr.Markdown(label="Classification (P or NP)")
+    
+    classify_button.click(pvnsp, inputs=problem_input, outputs=[classification_output])
+    
+    evaluate_button = gr.Button("Evaluate Recombination Complexity")
+    recombination_output = gr.Textbox(label="Recombination Complexity")
+    
+    evaluate_button.click(critic_analysis, inputs=classification_output, outputs=recombination_output)
+    
+    #results_button = gr.Button("Show Stored Results")
+    #results_display = gr.Textbox(label="Stored Results")
+    
+    #results_button.click(get_stored_results, outputs=results_display)
+
+app.launch(theme = gr.themes.Ocean())