# Bounded underapproximations

@article{Ganty2012BoundedU, title={Bounded underapproximations}, author={Pierre Ganty and Rupak Majumdar and Benjamin Monmege}, journal={Formal Methods in System Design}, year={2012}, volume={40}, pages={206-231} }

We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L′⊆L which has the same Parikh (commutative) image as L. Bounded languages, introduced by Ginsburg and Spanier, are subsets of regular languages of the form $w_{1}^{*}w_{2}^{*}\cdots w_{m}^{*}$ for some w1,…,wm∈Σ∗. In particular bounded context-free languages have nice structural and decidability properties. Our proof proceeds in two parts…

## 43 Citations

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This work presents a simple set of axioms for predicates that can express unboundedness properties and shows decidability of (i)~separability by bounded regular languages, (ii)~unboundedness of occurring factors from a language $K$ with mild conditions on $K$, and (iii) ~universality of the set of factors.

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## References

SHOWING 1-10 OF 42 REFERENCES

Some Decision Problems Concerning Semilinearity and Commutation

- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 2002

If the languages defined by M are effectively semilinear, then so are the languagesdefined by Mc, and, hence, their emptiness problem is decidable, and this work proves a surprising undecidability result for commutation of languages.

Context-Bounded Model Checking of Concurrent Software

- Computer ScienceTACAS
- 2005

This paper proves that the problem of verifying a concurrent boolean program is decidable, even in the presence of unbounded parallelism, if the analysis is restricted to executions in which the number of context switches is bounded by an arbitrary constant.

A generic approach to the static analysis of concurrent programs with procedures

- Computer Science, MathematicsPOPL '03
- 2003

An algebraic framework for defining abstractions (upper approximations) of context-free languages is proposed, which considers two classes of abstractions: finite-chain abstractions and commutative abstractions corresponding to classes of languages that contain a word if and only if they contain all its permutations.

Symbolic Context-Bounded Analysis of Multithreaded Java Programs

- Computer ScienceSPIN
- 2008

This paper proposes an improvement that overcomes the undecidable reachability problem for programs with both recursive procedures and multiple threads with shared memory and implemented the approach in the tool jMoped and reports on experiments.

Parikhʼs theorem: A simple and direct automaton construction

- Computer ScienceInf. Process. Lett.
- 2011

Introduction to automata theory, languages, and computation, 2nd edition

- Computer ScienceSIGA
- 2001

The introduction to formal languages and automata wasolutionary rather than rcvolrrtionary and addressed Initially, I felt that giving solutions to exercises was undesirable hecause it lirrritcd the Chapter 1 fntroduction to the Theory of Computation.

Iterating Octagons

- Computer ScienceTACAS
- 2009

It is proved that the transitive closure of a non-deterministic octagonal relation using integer counters can be expressed in Presburger arithmetic, which means that the reachability problem is decidable for flat counter automata with octagonal transition relations.

Model Checking Recursive Programs with Numeric Data Types

- Computer ScienceCAV
- 2011

This paper pinpoints the decidability/complexity of reachability and linear/branching time model checking over PDS with reversal-bounded counters (PCo), and shows reachability over PCo is NP-complete, while LTL is coNEXP-complete (coNP-complete for fixed formulas).

On Flatness for 2-Dimensional Vector Addition Systems with States

- Computer ScienceCONCUR
- 2004

2-dim VASS are flat (i.e. they “intrinsically” contain no nested loops), and it is obtained that – forward, backward and binary – reachability sets are effectively semilinear for the class of 2-Dim VASS, and that these sets can be computed using generic acceleration techniques.