Undecidable problem

About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.

On decidability of the control reachability problem in the asynchronous π-calculus

Abstract: We study the decidability of the control reachability problem for various fragments of the asynchronous π-calculus. We consider the combination of three main features: name generation, name mobility, and unbounded control. We show that the combination of name generation with either name mobility or unbounded control leads to an undecidable fragment. On the other hand, we prove that name generation with unique receiver and bounded input (a condition weaker than bounded control) is decidable by reduction to the coverability problem for Petri nets with transfer (and back).

On the decidability of phase ordering problem in optimizing compilation

Abstract: We are interested in the computing frontier around an essential question about compiler construction: having a program P and a set M of non parametric compiler optimization modules (called also phases), is it possible to find a sequence s of these phases such that the performance (execution time for instance) of the final generated program P′ is "optimal" ? We prove in this article that this problem is undecidable in two general schemes of optimizing compilation: iterative compilation and library optimization/generation. Fortunately, we give some simplified cases when this problem be-comes decidable, and we provide some algorithms (not necessary efficient) that can answer our main question. Another essential question that we are interested in is parame-ters space exploration in optimizing compilation (tuning optimizing compilation parameters). In this case, we assume a fixed sequence of optimization, but each optimization phase is allowed to have a parameter. We try to figure out how to compute the best parameter values for all program transformations when the compilation sequence is given. We also prove that this general problem is undecidable and we provide some simplified decidable instances.

Deciding Unambiguity and Sequentiality of Polynomially Ambiguous Min-Plus Automata

Abstract: This paper solves the unambiguity and the sequentiality problem for polynomially ambiguous min-plus automata. This result is proved through a decidable algebraic characterization involving so-called metatransitions and an application of results from the structure theory of finite semigroups. It is noteworthy that the equivalence problem is known to be undecidable for polynomially ambiguous automata.

Graph Logics with Rational Relations

Abstract: We investigate some basic questions about the interaction of regular and ra- tional relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subsequence. Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the gener- alized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersec- tion problem with regular relations is either undecidable (e.g., for subword or sux, and some generalizations), or decidable with non-primitive-recursive complexity (e.g., for sub- sequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the sim- plest problem related to verifying lossy channel systems that has non-primitive-recursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classies them into either eciently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions.