Multiphase ranking functions (MΦRFs) are tuples f 1 , . . . , f d of linear functions that are often used to prove termination of loops in which the computation progresses through a number of "phases". Our work provides new insights regarding such functions for loops described by a conjunction of linear constraints (Single-Path Constraint loops). The decision problem existence of a MΦRF asks to determine whether a given SLC loop admits a MΦRF; and the corresponding bounded decision problem restricts the search to MΦRFs of depth d, where the parameter d is part of the input. The algorithmic and complexity aspects of the bounded problem have been completely settled in a recent work. In this paper we make progress regarding the existence problem, without a given depth bound. In particular, we present an approach that reveals some important insights into the structure of these functions. Interestingly, it relates the problem of seeking MΦRFs to that of seeking recurrent sets (used to prove non-termination). It also helps in identifying classes of loops for which MΦRFs are sufficient. Our research has led to a new representation for single-path loops, the difference polyhedron replacing the customary transition polyhedron. This representation yields new insights on MΦRFs and SLC loops in general. For example, a result on bounded SLC loops becomes straightforward.

Control-flow refinement refers to program transformations whose purpose is to make implicit control-flow explicit, and is used in the context of program analysis to increase precision. Several techniques have been suggested for different programming models, typically tailored to improving precision for a particular analysis. In this paper we explore the use of partial evaluation of Horn clauses as a general-purpose technique for control-flow refinement for integer transitions systems. These are control-flow graphs where edges are annotated with linear constraints describing transitions between corresponding nodes, and they are used in many program analysis tools. Using partial evaluation for control-flow refinement has the clear advantage over other approaches in that soundness follows from the general properties of partial evaluation; in particular, properties such as termination and complexity are preserved. We use a partial evaluation algorithm incorporating property-based abstraction, and show how the right choice of properties allows us to prove termination and to infer complexity of challenging programs that cannot be handled by state-of-the-art tools. We report on the integration of the technique in a termination analyzer, and its use as a preprocessing step for several cost analyzers.

In this paper we describe EasyInterface, an open-source toolkit for rapid development of web-based graphical user interfaces (GUIs). This toolkit addresses the need of researchers to make their research prototype tools available to the community, and integrating them in a common environment, rapidly and without being familiar with web programming or GUI libraries in general. If a tool can be executed from a command-line and its output goes to the standard output, then in few minutes one can make it accessible via a web-interface or within Eclipse. Moreover, the toolkit defines a text-based language that can be used to get more sophisticated GUIs, e.g., syntax highlighting, dialog boxes, user interactions, etc. EasyInterface was originally developed for building a common frontend for tools developed in the Envisage [4] project.

Programs with multiphase control-flow are programs where the execution passes through several (possibly implicit) phases. Proving termination of such programs (or inferring corresponding runtime bounds) is often challenging since it requires reasoning on these phases separately. In this paper we discuss techniques for proving termination of such programs, in particular: (1) using multiphase ranking functions, where we will discuss theoretical aspects of such ranking functions for several kinds of program representations; and (2) using control-flow refinement, in particular partial evaluation of Constrained Horn Clauses, to simplify the control-flow allowing, among other things, to prove termination with simpler ranking functions.

No abstract