Related papers: Unrestricted Termination and Non-Termination Argum…
Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
We define a language-independent model of nondeterministic quantum programs in which a quantum program consists of a finite set of quantum processes. These processes are represented by quantum Markov chains over the common state space. An…
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…
The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The…
Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure)…
Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different…
Termination of logic programs with negated body atoms (here called general logic programs) is an important topic. One reason is that many computational mechanisms used to process negated atoms, like Clark's negation as failure and Chan's…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…
We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
We propose an automated method for proving termination of $\pi$-calculus processes, based on a reduction to termination of sequential programs: we translate a $\pi$-calculus process to a sequential program, so that the termination of the…
Determining whether a program terminates is a core challenge in program analysis with direct implications for correctness, verification, and security. We investigate whether transformer architectures can recognise termination patterns…
The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…
We present a new kind of nontermination argument, called geometric nontermination argument. The geometric nontermination argument is a finite representation of an infinite execution that has the form of a sum of several geometric series.…