Faster Algorithms for Algebraic Path Properties in Recursive State Machines with Constant Treewidth

Abstract

Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, etc. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring, and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, etc. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in a very important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect that we consider is that the control flow graphs for most programs have constant treewidth.Our main contributions are simple and implementable algorithms that support multiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing, but can answer subsequent queries significantly faster as compared to the current best-known solutions for several important problems, such as interprocedural reachability and shortest path. We provide a prototype implementation for interprocedural reachability and intraprocedural shortest path that gives a significant speed-up on several benchmarks.

JTDec: A Tool for Tree Decompositions in Soot

“…(2) The balanced tree-decompositions have been crucial in algorithms for interprocedural analysis [9] and verification of quantitative properties in graphs [5]. (3) The notion of (α, β, γ) tree-decompositions has been used in algorithmic dataflow analysis of concurrent programs [8].…”

“…In this case the log in stderr is: [JTDec] [createTreeDec] Obtaining CFG of the method [JTDec] [createTreeDec] CFG obtained [JTDec] [createTreeDec] The lines were numbered as follows: [JTDec] [createTreeDec] 1: n := @parameter0: int [JTDec] [JTDec] [createTreeDec] Creating a list of neighbors of each node [JTDec] [createTreeDec] successors are: {1= [2], 2= [3], 3= [4,5], 4=[21], 5= [6], 6= [7], 7= [8,9], 8= [14], 9= [10], 10= [11], 11= [12], 12= [13] [JTDec] [createTreeDec] neighbors are:{1= [2], 2= [1,3,20], 3= [2,4,5], 4= [3,21], 5= [3,6], 6= [5,7], 7= [6,8,9], 8= [7,14], 9= [7,10], 10= [9,11], 11= [10,12], 12= [11,13], 13= [19,12], 14= [8,15], 15= [16,14], 17...…”

“…Finally a tree decomposition is created by Algorithm 4 and is printed at the very end of the log. This can be done by simply printing the resulting JTDecTree, i.e., the code children: {1= [1,2], 2= [3], 3= [4,22], 4= [21,5], 5= [6], 6= [7], 7= [19,8,13], 8= [9], 9= [10], 10= [11], 11= [12], 12= [18], 13= [14], 14= [15] [17,18,7], 10= [17,16,7], 11= [16,7,15], 12= [7,14,15], 13= [19,7,13], 14= [7,12,13], 15= [7,11,12], 17= [7,9,10], 16= [7,10,11], 19= [3,6,7], 18= [7,8,14] {1=22, 2=3, 3=4, 4=21, 5=20, 6=19, 7=7...…”

“…Recently it was shown for problems in quantitative verification the constant treewidth can be exploited to design much faster algorithms [5], as well as improve space usage [7]. decomposition; and (b) balance a constant-width tree decomposition Balanced tree decompositions are required to support fast dynamic algorithms (i.e., algorithms that support fast updates given small changes in the input graph) [9] as well as for intraprocedural analysis of concurrent programs [8].…”

Algorithms for algebraic path properties in concurrent systems of constant treewidth components

“…A topic of widespread interest in the programming languages community is that of on-demand analysis [5,24,30,44,60,64,65,68,77,78]. Such analysis has several advantages, such as (quoting from [44,65]) (i) narrowing down the focus to specific points of interest, (ii) narrowing down the focus to specific dataflow facts of interest, (iii) reducing work in preliminary phases, (iv) sidestepping incremental updating problems, and (v) offering demand analysis as a user-level operation.…”