Acceptability with general orderings

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program termination analysis, but we apply these orderings directly to the logic program and not to the term-rewrite system obtained through some transformation. We define some variants of acceptability, based on general orderings, and show how they are equivalent to LD-termination. We develop a demand driven, constraint-based approach to verify these acceptability-variants. The advantage of the approach over standard acceptability is that in some cases, where complex level mappings are needed, fairly simple orderings may be easily generated. The advantage over transformational approaches is that it avoids the transformation step all together. {\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the Future

Управління виробничими запасами на підприємстві (на матеріалах ПрАТ «Детвілер Ущільнюючі Технології України»)

. The second-order matching problem is the problem of determining, for a finite set {#t i , s i # | i # I} of pairs of a second-order term t i and a first-order closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I . It is well-known that the second-order matching problem is NP-complete. In this paper, we introduce the following restrictions of a matching expression: k-ary, k-fv , predicate, ground , and function-free. Then, we show that the second-order matching problem is NP-complete for a unary predicate, a unary ground, a ternary function-free predicate, a binary function-free ground, and an 1-fv predicate matching expressions, while it is solvable in polynomial time for a binary function-free predicate, a unary function-free, a k-fv function-free (k # 0), and a ground predicate matching expressions. 1 Introduction The unification problem is the problem of determining whether or not any two ter..

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

Quantifier-Free Interpolation of a Theory of Arrays

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality

Lynx: A Programmatic SAT Solver for the RNA-folding Problem

15th International Conference, Trento, Italy, June 17-20, 2012. ProceedingsThis paper introduces Lynx, an incremental programmatic SAT solver that allows non-expert users to introduce domain-specific code into modern conflict-driven clause-learning (CDCL) SAT solvers, thus enabling users to guide the behavior of the solver. The key idea of Lynx is a callback interface that enables non-expert users to specialize the SAT solver to a class of Boolean instances. The user writes specialized code for a class of Boolean formulas, which is periodically called by Lynx’s search routine in its inner loop through the callback interface. The user-provided code is allowed to examine partial solutions generated by the solver during its search, and to respond by adding CNF clauses back to the solver dynamically and incrementally. Thus, the user-provided code can specialize and influence the solver’s search in a highly targeted fashion. While the power of incremental SAT solvers has been amply demonstrated in the SAT literature and in the context of DPLL(T), it has not been previously made available as a programmatic API that is easy to use for non-expert users. Lynx’s callback interface is a simple yet very effective strategy that addresses this need. We demonstrate the benefits of Lynx through a case-study from computational biology, namely, the RNA secondary structure prediction problem. The constraints that make up this problem fall into two categories: structural constraints, which describe properties of the biological structure of the solution, and energetic constraints, which encode quantitative requirements that the solution must satisfy. We show that by introducing structural constraints on-demand through user provided code we can achieve, in comparison with standard SAT approaches, upto 30x reduction in memory usage and upto 100x reduction in time

Membrane association and remodeling by intraflagellar transport protein IFT172.

The cilium is an organelle used for motility and cellular signaling. Intraflagellar transport (IFT) is a process to move ciliary building blocks and signaling components into the cilium. How IFT controls the movement of ciliary components is currently poorly understood. IFT172 is the largest IFT subunit essential for ciliogenesis. Due to its large size, the characterization of IFT172 has been challenging. Using giant unilamellar vesicles (GUVs), we show that IFT172 is a membrane-interacting protein with the ability to remodel large membranes into small vesicles. Purified IFT172 has an architecture of two globular domains with a long rod-like protrusion, resembling the domain organization of coatomer proteins such as COPI-II or clathrin. IFT172 adopts two different conformations that can be manipulated by lipids or detergents: 1) an extended elongated conformation and 2) a globular closed architecture. Interestingly, the association of IFT172 with membranes is mutually exclusive with IFT57, implicating multiple functions for IFT172 within IFT

Kinetic model of the aggregation of alpha-synuclein provides insights into prion-like spreading.

The protein alpha-synuclein (αS) self-assembles into small oligomeric species and subsequently into amyloid fibrils that accumulate and proliferate during the development of Parkinson's disease. However, the quantitative characterization of the aggregation and spreading of αS remains challenging to achieve. Previously, we identified a conformational conversion step leading from the initially formed oligomers to more compact oligomers preceding fibril formation. Here, by a combination of single-molecule fluorescence measurements and kinetic analysis, we find that the reaction in solution involves two unimolecular structural conversion steps, from the disordered to more compact oligomers and then to fibrils, which can elongate by further monomer addition. We have obtained individual rate constants for these key microscopic steps by applying a global kinetic analysis to both the decrease in the concentration of monomeric protein molecules and the increase in oligomer concentrations over a 0.5-140-µM range of αS. The resulting explicit kinetic model of αS aggregation has been used to quantitatively explore seeding the reaction by either the compact oligomers or fibrils. Our predictions reveal that, although fibrils are more effective at seeding than oligomers, very high numbers of seeds of either type, of the order of 10(4), are required to achieve efficient seeding and bypass the slow generation of aggregates through primary nucleation. Complementary cellular experiments demonstrated that two orders of magnitude lower numbers of oligomers were sufficient to generate high levels of reactive oxygen species, suggesting that effective templated seeding is likely to require both the presence of template aggregates and conditions of cellular stress.We thank Dr. Nadia Shivji and Beata Blaszczyk for ɑS protein expression, Dr. Peter Jönsson for help with preliminary TIRFM imaging experiments, Chris Taylor for help with preliminary autodilution experiments and Prof. Michel Goedert for critical reading of the manuscript. M.I. is funded by Dr. Tayyeb-Hussain Scholarship. G.A.G. is funded by the Schiff Foundation . S.G. is funded through a Wellcome Trust Intermediate Clinical Fellowship. Funding from the Frances and Augustus Newman Foundation, the European Research Council and the Biothechnology and Biophysical Sciences Research Council is gratefully acknowledged.This is the author accepted manuscript. The final version is available from the National Academy of Sciences via http://dx.doi.org/10.1073/pnas.152412811