On the Path-Width of Integer Linear Programming

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path- width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Constraint LTL Satisfiability Checking without Automata

This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short). The technique is based on the concept of bounded satisfiability, and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of quantifier-free equality and uninterpreted functions combined with D. Similarly to standard LTL, where bounded model-checking and SAT-solvers can be used as an alternative to automata-theoretic approaches to model-checking, our approach allows users to solve the satisfiability problem for CLTLB(D) formulae through SMT-solving techniques, rather than by checking the emptiness of the language of a suitable automaton A_{\phi}. The technique is effective, and it has been implemented in our Zot formal verification tool.Comment: 39 page

A Combinatorial Parametric Engineering Model for Solid Freeform Fabrication

Fabricated parts are often represented as compact connected smooth 3-manifolds with boundary, where the boundaries consist of compact smooth 2-manifolds. This class of mathematical structures includes topological spaces with enclosed voids and tunnels. Useful information about these structures are coded into level functions (Morse functions) which map points in the 3-manifold onto their height above a fixed plane. By definition, Morse functions are smooth functions, all of whose critical points are nondegenerate. This information is presented by the Reeb graph construction that develops a topologically informative skeleton of the manifold whose nodes are the critical points of the Morse function and whose edges are associated with the connected components between critical slices. This approach accurately captures the SFF process: using a solid geometric model of the part, defining surface boundaries; selecting a part orientation; forming planar slices, decomposing the solid into a sequence of thin cross-sectional polyhedral layers; and then fabricating the part by producing the polyhedra by additive manufacturing. This note will define a qualitative and combinatorial parametric engineering model of the SFF part design process. The objects under study will be abstract simplicial complexes K with boundary ∂K. Systems of labeled 2-surfaces in K, called slices, will be associated with the cross-sectional polyhedral layers. The labeled slices are mapped into a family of digraph automata, which, unlike cellular automata, are defined not on regular lattices with simple connectivities (cells usually have either 4 or 8 cell neighborhoods) but on unrestricted digraphs whose connectivities are irregular and more complicated.Mechanical Engineerin

A Component-oriented Framework for Autonomous Agents

The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a larger system that exhibits their collective behavior in a meaningful way. We propose an automaton-based paradigm for compositional design of such systems where an action is accompanied by one or more preferences. At run-time, these preferences provide a natural fallback mechanism for the component, while at design-time they can be used to reason about the behavior of the component in an uncertain physical world. Using structures that tell us how to compose preferences and actions, we can compose formal representations of individual components or agents to obtain a representation of the composed system. We extend Linear Temporal Logic with two unary connectives that reflect the compositional structure of the actions, and show how it can be used to diagnose undesired behavior by tracing the falsification of a specification back to one or more culpable components

Decompositions of Grammar Constraints

A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive constraints. We can then, for instance, use state of the art SAT solvers and profit from their advanced features like fast unit propagation, clause learning, and conflict-based search heuristics. This approach holds promise for solving combinatorial problems in scheduling, rostering, and configuration, as well as problems in more diverse areas like bioinformatics, software testing and natural language processing. In addition, decomposition may be an effective method to propagate other global constraints.Comment: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligenc