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Christoph Weidenbach - One of the best experts on this subject based on the ideXlab platform.

  • on the combination of the bernays schonfinkel ramsey fragment with simple linear integer arithmetic
    Conference on Automated Deduction, 2017
    Co-Authors: Matthias Horbach, Marco Voigt, Christoph Weidenbach
    Abstract:

    In general, first-Order Predicate Logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Schonfinkel-Ramsey fragment (\(\exists ^* \forall ^*\)-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma’s array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances.

Takafumi Aoki - One of the best experts on this subject based on the ideXlab platform.

  • formal approach for verifying galois field arithmetic circuits of higher degrees
    IEEE Transactions on Computers, 2017
    Co-Authors: Rei Ueno, Yukihiro Sugawara, Takafumi Aoki
    Abstract:

    This paper presents an efficient approach to verifying higher-degree Galois-field (GF) arithmetic circuits. The proposed method describes GF arithmetic circuits using a mathematical graph-based representation and verifies them by a combination of algebraic transformations and a new verification method based on natural deduction for first-Order Predicate Logic with equal sign. The natural deduction method can verify one type of higher-degree GF arithmetic circuit efficiently while the existing methods require an enormous amount of time, if they can verify them at all. In this paper, we first apply the proposed method to the design and verification of various Reed-Solomon (RS) code decoders. We confirm that the proposed method can verify RS decoders with higher-degree functions while the existing method needs a lot of time or fail. In particular, we show that the proposed method can be applied to practical decoders with 8-bit symbols, which are performed with up to 2,040-bit operands. We then demonstrate the design and verification of the Advanced Encryption Standard (AES) encryption and decryption processors. As a result, the proposed method successfully verifies the AES decryption datapath while an existing method fails.

  • An Efficient Approach to Verifying Galois-Field Arithmetic Circuits of Higher Degrees and Its Application to ECC Decoders
    2014 IEEE 44th International Symposium on Multiple-Valued Logic, 2014
    Co-Authors: Rei Ueno, Kotaro Okamoto, Naofumi Hommam, Takafumi Aoki
    Abstract:

    This paper presents an efficient approach to verifying higher-degree Galois-Field(GF) arithmetic circuits. The proposed method describes GF arithmetic circuits by graph-based representation, and verifies them by a combination of algebraic method with a new verification method based on natural deduction for the first-Order Predicate Logic with equal sign. The natural deduction method can verify kind of higher-degree GF arithmetic circuits efficiently while the conventional methods requires enormous time to verify them or sometimes cannot verify them. In this paper, we apply the proposed method to the design and verifications of various Reed-Solomon (RS) code decoders. We confirm that the proposed method can verify RS code decoders with higher-degree functions while the conventional method fails. In particular, we show that the proposed method can be applied to practical decoders with 8-bit symbols.

Matthias Horbach - One of the best experts on this subject based on the ideXlab platform.

  • on the combination of the bernays schonfinkel ramsey fragment with simple linear integer arithmetic
    Conference on Automated Deduction, 2017
    Co-Authors: Matthias Horbach, Marco Voigt, Christoph Weidenbach
    Abstract:

    In general, first-Order Predicate Logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Schonfinkel-Ramsey fragment (\(\exists ^* \forall ^*\)-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma’s array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances.

Ravi Sandhu - One of the best experts on this subject based on the ideXlab platform.

  • Role-based authorization constraints specification
    ACM Transactions on Information and System Security, 2000
    Co-Authors: Gail-joon Ahn, Ravi Sandhu
    Abstract:

    Constraints are an important aspect of role-based access control (RBAC) and are often regarded as one of the principal motivations behind RBAC. Although the importance of contraints in RBAC has been recogni zed for a long time, they have not recieved much attention. In this article, we introduce an intuitive formal language for specifying role-based authorization constraints named RCL 2000 including its basic elements, syntax, and semantics. We give soundness and completeness proofs for RCL 2000 relative to a restricted form of first-Order Predicate Logic. Also, we show how previously identified role-based authorization constraints such as separtation of duty (SOD) can be expressed in our language. Moreover, we show there are other significant SOD properties that have not been previously identified in the literature. Our work shows that there are many alternate formulations of even the simplest SOD properties, with varying degree of flexibility and assurance. Our language provides us a rigorous foundation for systematic study of role-based authorization constraints.

  • the rcl 2000 language for specifying role based authorization constraints
    2000
    Co-Authors: Gail-joon Ahn, Ravi Sandhu
    Abstract:

    Authorization constraints (also simply called constraints) are an important aspect of role-based access control (RBAC), since they can be argued to be one of the principal motivations behind RBAC. Although the importance of constraints in RBAC has been recognized for a long time, they have not received much attention in research literature, while role hierarchies have been practiced and discussed at considerable length. Most prior work has focused on separation of duty (SOD) constraints enumerating many variations. In this dissertation, we describe a framework for specifying authorization constraints in role-based systems. To specify these constraints, we need an appropriate language as well as some system functions. We propose a simple and intuitive language, RCL 2000 (Role-based Constraints Language 2000), to specify constraints in an intuitive and useful way in role-based systems. The formal semantics for this language is based on its translation to a restricted form of first Order Predicate Logic. With this language we show how we can express the previous SOD constraints discovering newly identified properties, such as permission-centric constraints. We also define new forms of SOD, especially with role hierarchies. To illustrate the power of RCL 2000 we specify constraints which have been identified in simulations of Lattice-based access control, Chinese Wall, and Discretionary access control policy in RBAC. Moreover, we separate role-based constraints into two major classes: Prohibition Constraints and Obligation Constraints. We characterize a subset of these classes from our specification of role-based constraints. Our work also shows that it is futile to try to enumerate all constraints because there are too many possibilities and variations; instead, we should pursue an intuitively simple yet rigorous language, such as RCL 2000 , for specifying constraints.

Weidenbach Christoph - One of the best experts on this subject based on the ideXlab platform.

  • Bernays-Schoenfinkel-Ramsey with Simple Bounds is NEXPTIME-complete
    2020
    Co-Authors: Voigt Marco, Weidenbach Christoph
    Abstract:

    First-Order Predicate Logic extended with linear arithmetic is undecidable, in general. We show that the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment extended with linear arithmetic restricted to simple bounds (SB) is decidable through finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures for BSR(SB). Satisfiability of BSR(SB) compared to BSR remains NEXPTIME-complete. The decidability result is almost tight because BSR is undecidable if extended with linear difference inequations, simple additive inequations, quotient inequations and multiplicative inequations.Comment: This is a revised version of the initial arXiv submission. Although submitted in 2020, the last update of its contents dates back to June 201

  • On the Combination of the Bernays–Schönfinkel–Ramsey Fragment with Simple Linear Integer Arithmetic
    'Springer Science and Business Media LLC', 2017
    Co-Authors: Horbach Matthias, Voigt Marco, Weidenbach Christoph
    Abstract:

    International audienceIn general, first-Order Predicate Logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Schönfinkel-Ramsey fragment (∃ * ∀ *-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma's array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances

  • On the Combination of the Bernays-Sch\"onfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic
    2017
    Co-Authors: Horbach Matthias, Voigt Marco, Weidenbach Christoph
    Abstract:

    In general, first-Order Predicate Logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Sch\"onfinkel-Ramsey fragment ($\exists^* \forall^*$-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma's array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances.Comment: Extended version of the CADE 2017 paper having the same title, 29 page