Bisimulation Method Research Articles

Bisimulations of nonlinear feedback shift registers

This work investigates how to reduce nonlinear feedback shift registers (NFSRs) in combination with bisimulation method via semi-tensor product (STP). By considering a large-scale NFSR as a smaller-scale Boolean system utilising bisimulation relations, the computing complexity of the system can be decreased. On the one hand, the properties of the bisimulation relation between two different NFSRs are examined, while on the other hand, a necessary and sufficient condition is discovered, as well as a reduction strategy utilising bisimulation. Besides, it is talked about how NFSR properties spread throughout the reduction process. The nonsingularity, driven stability and other aspects of the original NFSR are confirmed to be preserved by the reduced Boolean system.

Verifying polymer reaction networks using bisimulation

The Chemical Reaction Network model has been proposed as a programming language for molecular programming. Methods to implement arbitrary CRNs using DNA strand displacement circuits have been investigated, as have methods to prove the correctness of those or other implementations. However, the stochastic Chemical Reaction Network model is provably not deterministically Turing-universal, that is, it is impossible to create a stochastic CRN where a given output molecule is produced if and only if an arbitrary Turing machine accepts. A DNA stack machine that can simulate arbitrary Turing machines with minimal slowdown deterministically has been proposed, but it uses unbounded polymers that cannot be modeled as a Chemical Reaction Network. We propose an extended version of a Chemical Reaction Network that models unbounded linear polymers made from a finite number of monomers. This Polymer Reaction Network model covers the DNA stack machine, as well as copy-tolerant Turing machines and some examples from biochemistry. We adapt the bisimulation method of verifying DNA implementations of Chemical Reaction Networks to our model, and use it to prove the correctness of the DNA stack machine implementation. We define a subclass of single-locus Polymer Reaction Networks and show that any member of that class can be bisimulated by a network using only four primitives, suggesting a method of DNA implementation. Finally, we prove that deciding whether an implementation is a bisimulation is Π20-complete, and thus undecidable in the general case, although it is tractable in many special cases of interest. We hope that the ability to model and verify implementations of Polymer Reaction Networks will aid in the rational design of molecular systems.

Bisimulation-based Consistency Checking on Syndrome Feng-Shi-Re-Bi in Rheumatoid Arthritis

Checking the consistency of knowledge items between textbook and clinical practice is very important for traditional Chinese medicine (TCM). According to the textbook of internal medicine of TCM, rheumatoid arthritis (RA) is a disease with four main syndromes (also called pattern) and Feng-Shi-Re-Bi is a minor one and the associated literature data are not rich. Bisimulation is an equivalence relationship/method in formal methods which can be used to compare the consistency of system's description and its behaviors. In TCM, knowledge items from textbook can be taken as system's description, and knowledge items from clinical practice can be taken as the behaviors of the system. For RA's Feng-Shi-Re-Bi syndrome, employing bisimulation method, the consistency of knowledge items between textbook and clinical practice have been checked. As a result, on Feng-Shi-Re-Bi syndrome, most knowledge items in textbook can be simulated by the clinical practice e.g., syndrome, symptom, herbal formula, herbal medicine. What's more, in clinical practice, there are also variations based on basic rules of traditional Chinese medicine. In brief, bisimulation is a proper method for consistency checking between TCM textbook and clinical practice.

Environmental bisimulations for higher-order languages

Developing a theory of bisimulation in higher-order languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with “up-to context” techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environment{} bisimulations , a form of bisimulation for higher-order languages, and its basic theory. We consider four representative calculi: pure λ-calculi (call-by-name and call-by-value), call-by-value λ-calculus with higher-order store, and then Higher-Order π-calculus. In each case: we present the basic properties of environment bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some up-to techniques, including up-to context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, Sumii-Pierce-Koutavas-Wand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with up-to techniques), or sophisticated methods such as Howe's for proving congruence. It also scales from the pure λ-calculi to the richer calculi with simple congruence proofs.

A bisimulation for type abstraction and recursion

We present a bisimulation method for proving the contextual equivalence of packages in λ-calculus with full existential and recursive types. Unlike traditional logical relations (either semantic or syntactic), our development is “elementary,” using only sets and relations and avoiding advanced machinery such as domain theory, admissibility, and TT-closure. Unlike other bisimulations, ours is complete even for existential types. The key idea is to consider sets of relations—instead of just relations—as bisimulations.

Symbolic Approach to the Analysis of Security Protocols

The specification and validation of security protocols often requires view- ing function calls - like encryption/decryption and the generation of fake messages - explicitly as actions within the process semantics. Following this approach, this paper introduces a symbolic framework based on value-passing processes able to handle sym- bolic values like fresh nonces, fresh keys, fake addresses and fake messages. The main idea in our approach is to assign to each value-passing process a formula describing the symbolic values conveyed by its semantics. In such symbolic processes, called con- strained processes, the formulas are drawn from a logic based on a message algebra equipped with encryption, signature and hashing primitives. The symbolic operational semantics of a constrained process is then established through semantic rules updating formulas by adding restrictions over the symbolic values, as required for the process to evolve. We then prove that the logic required from the semantic rules is decidable. We also define a bisimulation equivalence between constrained processes; this amounts to a generalisation of the standard bisimulation equivalence between (non-symbolic) value-passing processes. Finally, we provide a complete symbolic bisimulation method for constructing the bisimulation between constrained processes.