Algebraic Engineering

There is algebraic structure in time, computation and biological systems. Algebraic engineering exploits this structure to achieve better understanding and design. In this book, pure and applied results in semigroups, language theory and algebra are applied to areas ranging from circuit design to software engineering to biological evolution.

Sample Chapter(s)
Foreword (121 KB)
Algebra for Understanding (837 KB)

• Algebraic Engineering:
  • Algebra for Understanding (C L Nehaniv)
  • Hidden Algebraic Engineering (J A Goguen)
  • Delay Insensitivity and Ternary Simulation (J A Brzozowski)
• Dynamics and Time:
  • System Time and System Timing (V Varshavsky)
  • Semigroup Representations and Dynamical Systems (I K Rystsov)
  • The Monoid and the Band of a Petri Net (E Wilkeit)
  • One-Orbit Transformation Semigroups on Finite Sets (T Saito)
  • Analysis of Asynchronous Higher-Order Discrete Neural Networks (Y Kobuchi)
• Biological Systems:
  • Complex Adaptations and the Structure of Recombination Spaces (G P Wagner & P F Stadler)
  • Life Morphogenesis in Models (A V Spirov)
• Complexity, Logic and Geometry:
  • Geometric Semigroup Theory (J McCammond & J Rhodes)
  • Decidable and Undeciable Problems for Semigroup Pseudovarieties (S I Kublanovsky)
  • Unimodular Regular Triangulations of (0,1)-Polytopes Associated with Finite Graphs (H Ohsugi)
  • Collapsing Theorem for the Slow-Growing and an Extended Hardy Hierarchies (O Takaki)
• Tilings and Codes:
  • A Change-of-Coordinates from Geometry to Algebra, Applied to Brick Tilings (J L King)
  • Introduction to Bicodes (K Hashiguchi, T Mizoguchi & N Nouda)
  • Brick Codes (W Moczurad)
  • Binary Distance Codes (K Hashiguchi, S Mouri, S Jimbo & H Yoshioka)
• Automata, Decompositions and Computation:
  • On Complete Systems of Automata (P Dömösi & C Nehaniv)
  • Blanket Algebra for Multiple-Valued Function Decomposition (J A Brzozowski & J J Lou)
  • Nets of Probabilistic Processors as a Powerful Means of Computation and Modelling (R Bukharaev)
  • K-Density and D-Continuity on Conditional Seminear-Rings (G Ciobanu & B Romila)
  • Parallel Computation: The Join of Pseudovarieties (B Steinberg)
  • Extended Finite Automata over Groups (V Mitrana & R Steibe)
  • Some Identities Related to Automata, Determinants, and Möbius Functions (V Diekert & Y Kobayashi)
• Software Systems:
  • Parallel Symbolic Simulation Using the Algebraic Programming System (A A Letichevsky, J V Kapitonova, A E Doroshenko & V A Volkov)
  • A Conceptual View on Updates of Object Bases (R Kaschek)
• Semigroup and Monoid Pseudovarieties:
  • Conditional Equations for Pseudovarieties (M V Volkov)
  • Type-I Subsemigroups, Revisited (K Henckell)
  • Power Semigroups: Results and Problems (J Almeida)
  • BG=PG, Revisited (K Henckell)
  • On Omega-Identities for Finite Semigroups (I Y Zhil'tsov)
• Semigroups and Algebra:
  • Normal Forms of Hypersubstitutions (K Denecke & J Koppitz)
  • Universal Aspects of Regular *-Semigroups (Z Jiang & P G Trotter)
  • Normal Forms of Hypersubstitutions (K Denecke & J Koppitz)
  • On Structurally Orthodox Semigroups (S J L Kopamu)
  • Kronecker Function Rings of Semistar-Operations on Semigroups and Rings (R Matsuda)
• Words, Languages and Grammars:
  • Shuffle Products and Related Operations on Languages (M Ito)
  • Decimations and Sturmian Words (J Justin & G Pirillo)
  • The Equational Properties of Reversal (Z Ésik, M Ito & M Katsura)
  • On the Relations between Multi-depth Grammars and Label-Distinguished Control Grammars (A Cherubini & P San Pietro)
  • New Pumping Lemma for Linear Indexed Languages (P Dömösi, J Duske & M Kudlek)
  • Modular Properties of Monoids and String-Rewriting Systems (F Otto)