In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step algorithms. This was accomplished on the basis of axiomatizations of these classes of algorithms. Here we extend the axiomatization and, in a companion paper, the proof, to cover interactive small-step algorithms that are not necessarily ordinary. This means that the algorithms (1) can complete a step without necessarily waiting for replies to all queries from that step and (2) can use not only the environment's replies but also the order in which the replies were received.
The inductive character of the context definition is unwound and analyzed in detail in @cite_27 . The answer functions which can occur as stages in the inductive construction of contexts are called . This captures the intuition of answer functions which can actually arise as records of interaction of an algorithm and its environment. Two causality relations (over the same state) are if they make the same answer functions well-founded. Equivalent causality relations have the same contexts but the converse is not in general true: intermediate intra-step behavior matters.
@cite_27
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A new form of SAT-based symbolic model checking is described. Instead of unrolling the transition relation, it incrementally generates clauses that are inductive relative to (and augment) stepwise approximate reachability information. In this way, the algorithm gradually refines the property, eventually producing either an inductive strengthening of the property or a counterexample trace. Our experimental studies show that induction is a powerful tool for generalizing the unreachability of given error states: it can refine away many states at once, and it is effective at focusing the proof search on aspects of the transition system relevant to the property. Furthermore, the incremental structure of the algorithm lends itself to a parallel implementation. We present a new co-inductive syntactic theory, eager normal form bisimilarity, for the untyped call-by-value lambda calculus extended with continuations and mutable references.We demonstrate that the associated bisimulation proof principle is easy to use and that it is a powerful tool for proving equivalences between recursive imperative higher-order programs.The theory is modular in the sense that eager normal form bisimilarity for each of the calculi extended with continuations and or mutable references is a fully abstract extension of eager normal form bisimilarity for its sub-calculi. For each calculus, we prove that eager normal form bisimilarity is a congruence and is sound with respect to contextual equivalence. Furthermore, for the calculus with both continuations and mutable references, we show that eager normal form bisimilarity is complete: it coincides with contextual equivalence. We examine the meaning of causality in calculi for mobile processes like the π-calculus, and we investigate the relationship between interleaving and causal semantics for such calculi. We separate two forms of causal dependencies on actions of π-calculus processes, called subject and object dependencies: The former originate from the nesting of prefixes and are propagated through interactions among processes (they are the only form of causal dependencies present in CCS-like languages); the latter originate from the binding mechanisms on names. We propose a notion of causal bisimulation which distinguishes processes which differ for the subject or for the object dependencies. We show that this causal equivalence can be reconducted to, or implemented into, the ordinary interleaving observation equivalence. We prove that our encoding is fully abstract w.r.t. the two behavioural equivalences. This allows us to exploit the simpler theory of the interleaving semantics to reason about the causal one. In [San94b] a similar programme is carried out for location bisimulation [BCHK91], a non-interleaving spatial-sensitive (as opposed to causal-sensitive) behavioural equivalence. The comparison between the encodings of causal bisimulation in this paper, and of location bisimulation in [San94b], evidences the similarities and the differences between these two equivalences. We propose Scene Graph Auto-Encoder (SGAE) that incorporates the language inductive bias into the encoder-decoder image captioning framework for more human-like captions. Intuitively, we humans use the inductive bias to compose collocations and contextual inference in discourse. For example, when we see the relation person on bike', it is natural to replace on' with ride' and infer person riding bike on a road' even the road' is not evident. Therefore, exploiting such bias as a language prior is expected to help the conventional encoder-decoder models less likely overfit to the dataset bias and focus on reasoning. Specifically, we use the scene graph --- a directed graph ( @math ) where an object node is connected by adjective nodes and relationship nodes --- to represent the complex structural layout of both image ( @math ) and sentence ( @math ). In the textual domain, we use SGAE to learn a dictionary ( @math ) that helps to reconstruct sentences in the @math pipeline, where @math encodes the desired language prior; in the vision-language domain, we use the shared @math to guide the encoder-decoder in the @math pipeline. Thanks to the scene graph representation and shared dictionary, the inductive bias is transferred across domains in principle. We validate the effectiveness of SGAE on the challenging MS-COCO image captioning benchmark, e.g., our SGAE-based single-model achieves a new state-of-the-art @math CIDEr-D on the Karpathy split, and a competitive @math CIDEr-D (c40) on the official server even compared to other ensemble models.