Efficient Pattern Matching in Python

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules. We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems

The N-end rule pathway controls multiple functions during Arabidopsis shoot and leaf development

The ubiquitin-dependent N-end rule pathway relates the in vivo half-life of a protein to the identity of its N-terminal residue. This proteolytic system is present in all organisms examined and has been shown to have a multitude of functions in animals and fungi. In plants, however, the functional understanding of the N-end rule pathway is only beginning. The N-end rule has a hierarchic structure. Destabilizing activity of N-terminal Asp, Glu, and (oxidized) Cys requires their conjugation to Arg by an arginyl–tRNA–protein transferase (R-transferase). The resulting N-terminal Arg is recognized by the pathway's E3 ubiquitin ligases, called “N-recognins.” Here, we show that the Arabidopsis R-transferases AtATE1 and AtATE2 regulate various aspects of leaf and shoot development. We also show that the previously identified N-recognin PROTEOLYSIS6 (PRT6) mediates these R-transferase-dependent activities. We further demonstrate that the arginylation branch of the N-end rule pathway plays a role in repressing the meristem-promoting BREVIPEDICELLUS (BP) gene in developing leaves. BP expression is known to be excluded from Arabidopsis leaves by the activities of the ASYMMETRIC LEAVES1 (AS1) transcription factor complex and the phytohormone auxin. Our results suggest that AtATE1 and AtATE2 act redundantly with AS1, but independently of auxin, in the control of leaf development

Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints

The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.Comment: 29 pages, long version of CADE-26 pape

Deduction with XOR Constraints in Security API Modelling

We introduce XOR constraints, and show how they enable a theorem prover to reason effectively about security critical subsystems which employ bitwise XOR. Our primary case study is the API of the IBM 4758 hardware security module. We also show how our technique can be applied to standard security protocols

The interaction of representation and reasoning

Automated reasoning is an enabling technology for many applications of informatics. These applications include verifying that a computer program meets its specification; enabling a robot to form a plan to achieve a task and answering questions by combining information from diverse sources, e.g. on the Internet, etc. How is automated reasoning possible? Firstly, knowledge of a domain must be stored in a computer, usually in the form of logical formulae. This knowledge might, for instance, have been entered manually, retrieved from the Internet or perceived in the environment via sensors, such as cameras. Secondly, rules of inference are applied to old knowledge to derive new knowledge. Automated reasoning techniques have been adapted from logic, a branch of mathematics that was originally designed to formalize the reasoning of humans, especially mathematicians. My special interest is in the way that representation and reasoning interact. Successful reasoning is dependent on appropriate representation of both knowledge and successful methods of reasoning. Failures of reasoning can suggest changes of representation. This process of representational change can also be automated. We will illustrate the automation of representational change by drawing on recent work in my research group

Attacking Group Protocols by Refuting Incorrect Inductive Conjectures

Automated tools for finding attacks on flawed security protocols often fail to deal adequately with group protocols. This is because the abstractions made to improve performance on fixed 2 or 3 party protocols either preclude the modelling of group protocols all together, or permit modelling only in a fixed scenario, which can prevent attacks from being discovered. This paper describes Coral, a tool for finding counterexamples to incorrect inductive conjectures, which we have used to model protocols for both group key agreement and group key management, without any restrictions on the scenario. We will show how we used Coral to discover 6 previously unknown attacks on 3 group protocols

Automatic Generation of Invariants for Circular Derivations in {SUP(LA)} 1

The hierarchic combination of linear arithmetic and firstorder logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA). For example, reachability problems for timed automata can be decided by SUP(LA) using an appropriate translation into FOL(LA). In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations. The rule enables decidability of more expressive fragments, including reachability for timed automata with unbounded integer variables. We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant problems

On the Expressivity and Applicability of Model Representation Formalisms

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism.Comment: 15 page

BIG enhances Arg/N-degron pathway-mediated protein degradation to regulate Arabidopsis hypoxia responses and suberin deposition

BIG/DARK OVEREXPRESSION OF CAB1/TRANSPORT INHIBITOR RESPONSE3 is a 0.5-MDa protein associated with multiple functions in Arabidopsis (Arabidopsis thaliana) signalling and development. However, the biochemical functions of BIG are unknown. We investigated a role for BIG in the Arg/N-degron pathways, in which substrate protein fate is influenced by the N-terminal (Nt) residue. We crossed a big loss-of-function allele to two N-degron pathway E3 ligase mutants, proteolysis6 (prt6) and prt1, and examined the stability of protein substrates. Stability of model substrates was enhanced in prt6-1 big-2 and prt1-1 big-2 relative to the respective single mutants and the abundance of the PRT6 physiological substrates, HYPOXIA-RESPONSIVE ERF2 (HRE2) and VERNALIZATION2 (VRN2) was similarly increased in prt6 big double mutants. Hypoxia marker expression was enhanced in prt6 big double mutants; this constitutive response required arginyltransferase activity and RAP-type ERFVII transcription factors. Transcriptomic analysis of roots not only demonstrated increased expression of multiple hypoxia-responsive genes in the double mutant relative to prt6, but also revealed other roles for PRT6 and BIG, including regulation of suberin deposition through both ERFVII-dependent and independent mechanisms, respectively. Our results show that BIG acts together with PRT6 to regulate the hypoxia response and broader processes in Arabidopsis