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  1. Deharbe, David ; Hyvarinen, Antti E. (Ed.)
    CDSAT (Conflict-Driven Satisfiability) is a paradigm for theory combination that works by coordinating theory modules to reason in the union of the theories in a conflict-driven manner. We generalize CDSAT to the case of nondisjoint theories by presenting a new CDSAT theory module for a theory of arrays with abstract length, which is an abstraction of the theory of arrays with length. The length function is a bridging function as it forces theories to share symbols, but the proposed abstraction limits the sharing to one predicate symbol. The CDSAT framework handles shared predicates with minimal changes, and the new module satisfies the CDSAT requirements, so that completeness is preserved.
    Free, publicly-accessible full text available August 11, 2023
  2. Abstract

    Search-based satisfiability procedures try to build a model of the input formula by simultaneously proposing candidate models and deriving new formulae implied by the input.Conflict-drivenprocedures perform non-trivial inferences only when resolving conflicts between formulæ and assignments representing the candidate model. CDSAT (Conflict-Driven SATisfiability) is a method for conflict-driven reasoning inunions of theories. It combines inference systems for individual theories astheory moduleswithin a solver for the union of the theories. This article augments CDSAT with a more generallemma learningcapability and withproof generation. Furthermore, theory modules for several theories of practical interest are shown to fulfill the requirements forcompletenessandterminationof CDSAT. Proof generation is accomplished by aproof-carryingversion of the CDSAT transition system that producesproof objectsin memory accommodating multiple proof formats. Alternatively, one can apply to CDSAT theLCF approach to proofsfrom interactive theorem proving, by defining a kernel of reasoning primitives that guarantees the correctness by construction of CDSAT proofs.

  3. We propose a novel passive learning approach, TeLex, to infer signal temporal logic (STL) formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. First, we present a template-driven learning approach that requires two inputs: a set of observed traces and a template STL formula. The unknown parameters in the template can include time-bounds of the temporal operators, as well as the thresholds in the inequality predicates. TeLEx finds the value of the unknown parameters such that the synthesized STL property is satisfied by all the provided traces and it is tight. This requirement of tightness is essential to generating interesting properties when only positive examples are provided and there is no option to actively query the dynamical system to discover the boundaries of legal behavior. We propose a novel quantitative semantics for satisfaction of STL properties which enables TeLEx to learn tight STL properties without multidimensional optimization. The proposed new metric is also smooth. This is critical to enable the use of gradient-based numerical optimization engines and it produces a 30x to 100x speed-up with respect to the state-of-art gradient-free optimization. Second, we present a novel technique for automatically learning the structuremore »of the STL formula by incrementally constructing more complex formula guided by the robustness metric of subformula. We demonstrate the effectiveness of the overall approach for learning STL formulas from only positive examples on a set of synthetic and real-world benchmarks.« less
  4. We propose an automatic synthesis technique to generate provably correct controllers of stochastic linear dynamical systems for Signal Temporal Logic (STL) specifications. While formal synthesis problems can be directly formulated as exists-forall constraints, the quantifier alternation restricts the scalability of such an approach. We use the duality between a system and its proof of correctness to partially alleviate this challenge. We decompose the controller synthesis into two subproblems, each addressing orthogonal concerns - stabilization with respect to the noise, and meeting the STL specification. The overall controller is a nested controller comprising of the feedback controller for noise cancellation and an open loop controller for STL satisfaction. The correct-by-construction compositional synthesis of this nested controller relies on using the guarantees of the feedback controller instead of the controller itself. We use a linear feedback controller as the stabilizing controller for linear systems with bounded additive noise and over-approximate its ellipsoid stability guarantee with a polytope. We then use this over-approximation to formulate a mixed-integer linear programming (MILP) problem to synthesize an open-loop controller that satisfies STL specifications.