Proving termination of sequential programs is an important problem, both for establishing the total correctness of systems and as a component of proving more general termination and liveness properties. We present a new algorithm, TREX, that determines if a sequential program terminates on all inputs. The key characteristic of TREX is that it alternates between refining an overapproximation and...

In bacteria, intrinsic termination signals cause disassembly of the highly stable elongating transcription complex (EC) over windows of two to three nucleotides after kilobases of RNA synthesis. Intrinsic termination is caused by the formation of a nascent RNA hairpin adjacent to a weak RNA-DNA hybrid within RNA polymerase (RNAP). Although the contributions of RNA and DNA sequences to terminati...

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often restricted to finding linear ranking functions over mathematical integers. This class of functions is insufficient for proving termination of many terminatin...

For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is presented for showing termination in this case. The method consists of the following steps: First, a nite abstract domain for representing the range of integers ...

In this paper, we present an approach to non-termination inference of logic programs. Our framework relies on an extension of the Lifting Theorem, where some specific argument positions can be instantiated while others are generalized. Atomic left looping queries are then generated bottom-up from selected subsets of the binary unfoldings of the program of interest. Then non-termination inferenc...

Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to AC-TRSs, and introduce new methods for effectively proving AC-termination. Since it is impossible to directly apply the notion of dependency pairs to AC-TRSs, we introduce the head ...

We used consensual qualitative research to analyze interviews with 12 clients about their termination from psychotherapy. Those who had positive termination experiences reported a strong therapeutic relationship and positive outcomes of therapy. They terminated primarily for logistical or financial reasons; their termination, post-termination plans, and feelings about termination were discussed...

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations very well known in the context of term rewrite systems (TRSs) to obtain new (non-transformational) termination analysis techniques for definite logic pro...

In an earlier work, a termination analyzer for Java bytecode was developed that translates a Java bytecode program into a constraint logic program and then proves the termination of the latter. An efficiency bottleneck of the termination analyzer is the construction of a proof of termination for the generated constraint logic program, which is often very large in size. In this paper, a set of p...

Poly(A) signals are required for efficient 3' end formation and transcriptional termination of most protein-encoding genes transcribed by RNA polymerase II. However, transcription can extend far beyond the poly(A) site before termination occurs. This implies the existence of further downstream termination signals. In mammals, a variety of sequence elements, in addition to the poly(A) site, have...