Topic
Undecidable problem
About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.
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TL;DR: It is shown that the reversibility problem is undecidable in case of two-dimensional CA, and it is proved that the corresponding surjectivity problem-the problem of deciding if the global function is surjective-is Undecidable for two- dimensional CA.
249 citations
05 Nov 2006
TL;DR: This paper proposes a new algorithm, Synergy, which combines testing and verification, and unifies several ideas from the literature, including counterexample-guided model checking, directed testing, and partition refinement.
Abstract: We consider the problem if a given program satisfies a specified safety property. Interesting programs have infinite state spaces, with inputs ranging over infinite domains, and for these programs the property checking problem is undecidable. Two broad approaches to property checking are testing and verification. Testing tries to find inputs and executions which demonstrate violations of the property. Verification tries to construct a formal proof which shows that all executions of the program satisfy the property. Testing works best when errors are easy to find, but it is often difficult to achieve sufficient coverage for correct programs. On the other hand, verification methods are most successful when proofs are easy to find, but they are often inefficient at discovering errors. We propose a new algorithm, Synergy, which combines testing and verification. Synergy unifies several ideas from the literature, including counterexample-guided model checking, directed testing, and partition refinement.This paper presents a description of the Synergy algorithm, its theoretical properties, a comparison with related algorithms, and a prototype implementation called Yogi.
245 citations
Proceedings Article•
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TL;DR: This article introduces the bounded synthesis approach, which makes it possible to traverse this immense search space in a structured manner and demonstrates that bounded synthesis solves many synthesis problems that were previously considered intractable.
Abstract: The bounded synthesis problem is to construct an implementation that satisfies a given temporal specification and a given bound on the number of states. We present a solution to the bounded synthesis problem for linear-time temporal logic (LTL), based on a novel emptiness-preserving translation from LTL to safety tree automata. For distributed architectures, where standard unbounded synthesis is in general undecidable, we show that bounded synthesis can be reduced to a SAT problem. As a result, we obtain an effective algorithm for the bounded synthesis from LTL specifications in arbitrary architectures. By iteratively increasing the bound, our construction can also be used as a semi-decision procedure for the unbounded synthesis problem.
243 citations
14 Mar 1997
TL;DR: These notes contain some high points from the recent book, emphasising what is different or novel with respect to more traditional treatments of computability and complexity theory, and some new results as well.
Abstract: A programming approach to computability and complexity theory yields proofs of central results that are sometimes more natural than the classical ones; and some new results as well. These notes contain some high points from the recent book [14], emphasising what is different or novel with respect to more traditional treatments. Topics include:
Kleene’s s-m-n theorem applied to compiling and compiler generation.
Proof that constant time factors do matter: for a natural computation model, problems solvable in linear time have a proper hierarchy, ordered by coefficient values. (In contrast to the “linear speedup” property of Turing machines.)
Results on which problems possess optimal algorithms, including Levin’s Search theorem (for the first time in book form).
Characterisations in programming terms of a wide range of complexity classes. These are intrinsic: without externally imposed space or time computation bounds.
Boolean program problems complete for PTIME, NPTIME, PSPACE.
242 citations
TL;DR: In this paper, it was shown that the robustness of linear systems under time-varying perturbations is undecidable, and the same is true for the stability of a simple class of hybrid systems.
234 citations