Related papers: Termination of oblivious chase is undecidable
Writing concurrent programs is notoriously hard due to scheduling non-determinism. The most common concurrency bugs are data races, which are accesses to a shared resource that can be executed concurrently. Dynamic data-race prediction is…
The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed $\lambda$-calculus, i.e. to solve the equation a = b where a and b are simply typed $\lambda$-terms and b is…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…
Since Cocke and Minsky proved 2-tag systems universal, they have been extensively used to prove the universality of numerous computational models. Unfortunately, all known algorithms give universal 2-tag systems that have a large number of…
We address the following decision problem. Given a numeration system $U$ and a $U$-recognizable set $X\subseteq\mathbb{N}$, i.e. the set of its greedy $U$-representations is recognized by a finite automaton, decide whether or not $X$ is…
We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to decidable as one can expect them to be: there exist sound…
We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
Sound exhaustiveness checking of pattern-matching is an essential feature of functional programming languages, and OCaml supports it for GADTs. However this check is incomplete, in that it may fail to detect that a pattern can match no…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of…
The set of pure terms which are typable in the $\lambda$$\Pi$-calculus in a given context is not recursive. So there is no general type inference algorithm for the programming language Elf and, in some cases, some type information has to be…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
The verification of concurrent programs under weak-memory models is a burgeoning effort, owing to the increasing adoption of weak memory in concurrent software and hardware. Release/Acquire has become the standard model for high-performance…
There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…
The termination behavior of probabilistic programs depends on the outcomes of random assignments. Almost sure termination (AST) is concerned with the question whether a program terminates with probability one on all possible inputs.…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
Data-centric dynamic systems are systems where both the process controlling the dynamics and the manipulation of data are equally central. In this paper we study verification of (first-order) mu-calculus variants over relational…